the american practical navigator table 2 natural trigonometric functions

TABLE Natural Trigonometric Functions 1′ sec Diff 1′ cot 29 29 29 29 29 30 29 29 29 29 29 29 29 29 29 29 30 29 29 29 29 29 29 29 29 29 29 30 29 29 29 29 29 29 29 29 29 29 30 29 29 29 29 29 29 29 29 29 29 30 29 29 29 29 29 29 29 29 29 30 Diff 1′ ∞ 3437.75 1718.87 1145.92 859.436 687.549 572.957 491.106 429.718 381.971 343.774 312.521 286.478 264.441 245.552 229.182 214.858 202.219 190.984 180.932 171.885 163.700 156.259 149.465 143.237 137.507 132.219 127.321 122.774 118.540 114.589 110.892 107.426 104.171 101.107 98.2179 95.4895 92.9085 90.4633 88.1436 85.9398 83.8435 81.8470 79.9434 78.1263 76.3900 74.7292 73.1390 71.6151 70.1533 68.7501 67.4019 66.1055 64.8580 63.6567 62.4992 61.3829 60.3058 59.2659 58.2612 57.2900 tan — — 1718.88 572.958 286.479 171.887 114.592 81.851 61.388 47.747 38.197 31.252 26.044 22.037 18.889 16.370 14.324 12.639 11.235 10.052 9.047 8.185 7.441 6.794 6.228 5.730 5.289 4.897 4.547 4.234 3.952 3.697 3.466 3.256 3.064 2.8890 2.7285 2.5810 2.4452 2.3198 2.2038 2.0963 1.9965 1.9036 1.8171 1.7363 1.6608 1.5902 1.5239 1.4617 1.4033 1.3482 1.2964 1.2475 1.2013 1.1576 1.1162 1.0771 1.0399 1.0047 0.9712 Diff 1′ sec 1.00000 00000 00000 00000 00000 1.00000 00000 00000 00000 00000 1.00000 00001 00001 00001 00001 1.00001 00001 00001 00001 00002 1.00002 00002 00002 00002 00002 1.00003 00003 00003 00003 00004 1.00004 00004 00004 00005 00005 1.00005 00005 00006 00006 00006 1.00007 00007 00007 00008 00008 1.00009 00009 00009 00010 00010 1.00011 00011 00011 00012 00012 1.00013 00013 00014 00014 00015 1.00015 csc Diff 1′ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 Diff 1′ cos 1.00000 00000 00000 00000 00000 1.00000 00000 00000 00000 00000 1.00000 99999 99999 99999 99999 0.99999 99999 99999 99999 99998 0.99998 99998 99998 99998 99998 0.99997 99997 99997 99997 99996 0.99996 99996 99996 99995 99995 0.99995 99995 99994 99994 99994 0.99993 99993 99993 99992 99992 0.99991 99991 99991 99990 99990 0.99989 99989 99989 99988 99988 0.99987 99987 99986 99986 99985 0.99985 sin Diff 1′ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 ′ 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 Diff 1′ 89° 1°➙ ′ 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 sin Diff 1′ csc Diff 1′ 0.01745 01774 01803 01832 01862 0.01891 01920 01949 01978 02007 0.02036 02065 02094 02123 02152 0.02181 02211 02240 02269 02298 0.02327 02356 02385 02414 02443 0.02472 02501 02530 02560 02589 0.02618 02647 02676 02705 02734 0.02763 02792 02821 02850 02879 0.02908 02938 02967 02996 03025 0.03054 03083 03112 03141 03170 0.03199 03228 03257 03286 03316 0.03345 03374 03403 03432 03461 0.03490 29 29 29 30 29 29 29 29 29 29 29 29 29 29 29 30 29 29 29 29 29 29 29 29 29 29 29 30 29 29 29 29 29 29 29 29 29 29 29 29 30 29 29 29 29 29 29 29 29 29 29 29 29 30 29 29 29 29 29 29 57.2987 56.3595 55.4505 54.5705 53.7179 52.8916 52.0903 51.3129 50.5584 49.8258 49.1141 48.4224 47.7500 47.0960 46.4596 45.8403 45.2372 44.6498 44.0775 43.5196 42.9757 42.4452 41.9277 41.4227 40.9296 40.4482 39.9780 5185 39.0696 38.6307 38.2016 37.7818 37.3713 36.9695 5763 36.1914 35.8145 4454 35.0838 34.7295 34.3823 34.0420 33.7083 3812 33.0603 32.7455 4367 32.1337 31.8362 5442 31.2576 30.9761 6996 4280 30.1612 29.8990 6414 3881 29.1392 28.8944 28.6537 9392 9089 8801 8526 8263 8013 7774 7545 7326 7117 6917 6724 6540 6363 6194 6031 5874 5723 5578 5439 5305 5175 5051 4930 4814 4702 4594 4490 4389 4291 4197 4106 4017 3932 3849 3769 3691 3616 3543 3472 3403 3336 3272 3209 3148 3088 3031 2974 2920 2867 2815 2765 2716 2668 2622 2577 2532 2490 2448 2407 ➙ Diff 0.00000 00029 00058 00087 00116 0.00145 00175 00204 00233 00262 0.00291 00320 00349 00378 00407 0.00436 00465 00495 00524 00553 0.00582 00611 00640 00669 00698 0.00727 00756 00785 00815 00844 0.00873 00902 00931 00960 00989 0.01018 01047 01076 01105 01135 0.01164 01193 01222 01251 01280 0.01309 01338 01367 01396 01425 0.01455 01484 01513 01542 01571 0.01600 01629 01658 01687 01716 0.01746 Diff 1′ 91°➙ cos Diff 1′ sec Diff 1′ tan 0.01746 01775 01804 01833 01862 0.01891 01920 01949 01978 02007 0.02036 02066 02095 02124 02153 0.02182 02211 02240 02269 02298 0.02328 02357 02386 02415 02444 0.02473 02502 02531 02560 02589 0.02619 02648 02677 02706 02735 0.02764 02793 02822 02851 02881 0.02910 02939 02968 02997 03026 0.03055 03084 03114 03143 03172 0.03201 03230 03259 03288 03317 0.03346 03376 03405 03434 03463 0.03492 cot Diff 1′ 29 29 29 29 29 29 29 29 29 29 30 29 29 29 29 29 29 29 29 30 29 29 29 29 29 29 29 29 29 30 29 29 29 29 29 29 29 29 30 29 29 29 29 29 29 29 30 29 29 29 29 29 29 29 29 30 29 29 29 29 Diff 1′ cot 57.2900 56.3506 55.4415 54.5613 53.7086 52.8821 52.0807 51.3032 50.5485 49.8157 49.1039 48.4121 47.7395 47.0853 46.4489 45.8294 45.2261 44.6386 44.0661 43.5081 42.9641 42.4335 41.9158 41.4106 40.9174 40.4358 39.9655 5059 39.0568 38.6177 38.1885 37.7686 37.3579 36.9560 5627 36.1776 35.8006 4313 35.0695 34.7151 34.3678 34.0273 33.6935 3662 33.0452 32.7303 4213 32.1181 31.8205 5284 31.2416 30.9599 6833 4116 30.1446 29.8823 6245 3711 29.1220 28.8771 28.6363 tan Diff 1′ 9394 9091 8802 8527 8265 8014 7775 7547 7328 7118 6918 6726 6542 6365 6195 6032 5875 5725 5580 5440 5306 5177 5052 4932 4816 4704 4596 4491 4390 4293 4198 4107 4019 3933 3851 3770 3693 3617 3544 3473 3405 3338 3273 3210 3149 3090 3032 2976 2921 2868 2816 2766 2717 2670 2623 2578 2534 2491 2449 2408 Diff 1′ sec 1.00015 00016 00016 00017 00017 1.00018 00018 00019 00020 00020 1.00021 00021 00022 00023 00023 1.00024 00024 00025 00026 00026 1.00027 00028 00028 00029 00030 1.00031 00031 00032 00033 00034 1.00034 00035 00036 00037 00037 1.00038 00039 00040 00041 00041 1.00042 00043 00044 00045 00046 1.00047 00048 00048 00049 00050 1.00051 00052 00053 00054 00055 1.00056 00057 00058 00059 00060 1.00061 csc Diff 1′ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Diff 1′ cos 178° 0.99985 99984 99984 99983 99983 0.99982 99982 99981 99980 99980 0.99979 99979 99978 99977 99977 0.99976 99976 99975 99974 99974 0.99973 99972 99972 99971 99970 0.99969 99969 99968 99967 99966 0.99966 99965 99964 99963 99963 0.99962 99961 99960 99959 99959 0.99958 99957 99956 99955 99954 0.99953 99952 99952 99951 99950 0.99949 99948 99947 99946 99945 0.99944 99943 99942 99941 99940 0.99939 sin Diff 1′ ′ 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Diff ➙ cos — — 1718.88 572.958 286.479 171.887 114.592 81.851 61.388 47.746 38.197 31.252 26.043 22.037 18.889 16.370 14.324 12.639 11.234 10.052 9.047 8.185 7.441 6.794 6.228 5.730 5.289 4.897 4.547 4.234 3.951 3.696 3.465 3.255 3.064 2.8888 2.7283 2.5808 2.4450 2.3196 2.2036 2.0961 1.9963 1.9035 1.8169 1.7362 1.6607 1.5900 1.5238 1.4616 1.4031 1.3481 1.2962 1.2473 1.2011 1.1574 1.1161 1.0769 1.0398 1.0046 0.9711 cot ➙ ➙ ∞ 3437.75 1718.87 1145.92 859.437 687.550 572.958 491.107 429.719 381.972 343.775 312.523 286.479 264.443 245.554 229.184 214.860 202.221 190.987 180.935 171.888 163.703 156.262 149.468 143.241 137.511 132.222 127.325 122.778 118.544 114.593 110.897 107.431 104.176 101.112 98.2230 95.4947 92.9139 90.4689 88.1492 85.9456 83.8495 81.8531 79.9497 78.1327 76.3966 74.7359 73.1458 71.6221 70.1605 68.7574 67.4093 66.1130 64.8657 63.6646 62.5072 61.3911 60.3141 59.2743 58.2698 57.2987 Diff 1′ ➙ 29 29 29 29 29 30 29 29 29 29 29 29 29 29 29 29 30 29 29 29 29 29 29 29 29 29 29 29 30 29 29 29 29 29 29 29 29 29 29 30 29 29 29 29 29 29 29 29 29 29 29 30 29 29 29 29 29 29 29 29 tan 1′ 88° 575 90°➙ 179° ➙ 0.00000 00029 00058 00087 00116 0.00145 00175 00204 00233 00262 0.00291 00320 00349 00378 00407 0.00436 00465 00495 00524 00553 0.00582 00611 00640 00669 00698 0.00727 00756 00785 00814 00844 0.00873 00902 00931 00960 00989 0.01018 01047 01076 01105 01134 0.01164 01193 01222 01251 01280 0.01309 01338 01367 01396 01425 0.01454 01483 01513 01542 01571 0.01600 01629 01658 01687 01716 0.01745 Diff 1′ ➙ csc ➙ Diff 1′ ➙ ➙ ′ 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 sin ➙ 0°➙ ➙ TABLE Natural Trigonometric Functions TABLE Natural Trigonometric Functions 1′ sec Diff 1′ cot Diff 1′ 28.6363 3994 28.1664 27.9372 7117 27.4899 2715 27.0566 26.8450 6367 26.4316 2296 26.0307 25.8348 6418 25.4517 2644 25.0798 24.8978 7185 24.5418 3675 1957 24.0263 23.8593 23.6945 5321 3718 2137 23.0577 22.9038 7519 6020 4541 3081 22.1640 22.0217 21.8813 7426 6056 21.4704 3369 2049 21.0747 20.9460 20.8188 6932 5691 4465 3253 20.2056 20.0872 19.9702 8546 7403 19.6273 5156 4051 2959 1879 19.0811 tan 2369 2330 2292 2255 2219 2184 2149 2116 2083 2051 2020 1989 1959 1930 1901 1873 1846 1819 1793 1768 1742 1718 1694 1670 1647 1625 1603 1581 1560 1539 1519 1499 1479 1460 1441 1423 1405 1387 1369 1352 1335 1319 1303 1287 1271 1256 1241 1226 1212 1198 1184 1170 1156 1143 1130 1117 1105 1092 1080 1068 Diff 1′ 1.00061 00062 00063 00064 00065 1.00066 00067 00068 00069 00070 1.00072 00073 00074 00075 00076 1.00077 00078 00079 00081 00082 1.00083 00084 00085 00087 00088 1.00089 00090 00091 00093 00094 1.00095 00097 00098 00099 00100 1.00102 00103 00104 00106 00107 1.00108 00110 00111 00113 00114 1.00115 00117 00118 00120 00121 1.00122 00124 00125 00127 00128 1.00130 00131 00133 00134 00136 1.00137 csc Diff 1′ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 2 1 2 2 Diff 1′ cos 0.99939 99938 99937 99936 99935 0.99934 99933 99932 99931 99930 0.99929 99927 99926 99925 99924 0.99923 99922 99921 99919 99918 0.99917 99916 99915 99913 99912 0.99911 99910 99909 99907 99906 0.99905 99904 99902 99901 99900 0.99898 99897 99896 99894 99893 0.99892 99890 99889 99888 99886 0.99885 99883 99882 99881 99879 0.99878 99876 99875 99873 99872 0.99870 99869 99867 99866 99864 0.99863 sin Diff 1′ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 2 2 2 ′ 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 Diff 1′ 87° 3°➙ ′ 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 sin Diff 1′ csc Diff 1′ 0.05234 05263 05292 05321 05350 0.05379 05408 05437 05466 05495 0.05524 05553 05582 05611 05640 0.05669 05698 05727 05756 05785 0.05814 05844 05873 05902 05931 0.05960 05989 06018 06047 06076 0.06105 06134 06163 06192 06221 0.06250 06279 06308 06337 06366 0.06395 06424 06453 06482 06511 0.06540 06569 06598 06627 06656 0.06685 06714 06743 06773 06802 0.06831 06860 06889 06918 06947 0.06976 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 30 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 30 29 29 29 29 29 29 29 19.1073 19.0019 18.8975 7944 6923 18.5914 4915 3927 2950 1983 18.1026 18.0079 17.9142 8215 7298 17.6389 5490 4600 3720 2848 17.1984 1130 17.0283 16.9446 8616 16.7794 6981 6175 5377 4587 16.3804 3029 2261 1500 16.0746 15.9999 9260 8527 7801 7081 15.6368 5661 4961 4267 3579 15.2898 2222 1553 0889 15.0231 14.9579 8932 8291 7656 7026 14.6401 5782 5168 4559 3955 14.3356 1055 1043 1032 1020 1009 999 988 977 967 957 947 937 927 918 908 899 890 881 872 863 855 846 838 830 822 814 806 798 790 783 775 768 761 754 747 740 733 726 720 713 707 700 694 688 682 676 670 664 658 652 647 641 635 630 625 619 614 609 604 599 ➙ Diff 29 29 29 30 29 29 29 29 29 29 29 30 29 29 29 29 29 29 30 29 29 29 29 29 29 30 29 29 29 29 29 29 30 29 29 29 29 29 29 30 29 29 29 29 29 30 29 29 29 29 29 29 30 29 29 29 29 29 30 29 sec 93°➙ cos Diff 1′ sec Diff 1′ tan 0.05241 05270 05299 05328 05357 0.05387 05416 05445 05474 05503 0.05533 05562 05591 05620 05649 0.05678 05708 05737 05766 05795 0.05824 05854 05883 05912 05941 0.05970 05999 06029 06058 06087 0.06116 06145 06175 06204 06233 0.06262 06291 06321 06350 06379 0.06408 06437 06467 06496 06525 0.06554 06584 06613 06642 06671 0.06700 06730 06759 06788 06817 0.06847 06876 06905 06934 06963 0.06993 cot Diff 1′ 29 29 29 29 30 29 29 29 29 30 29 29 29 29 29 30 29 29 29 29 30 29 29 29 29 29 30 29 29 29 29 30 29 29 29 29 30 29 29 29 29 30 29 29 29 30 29 29 29 29 30 29 29 29 30 29 29 29 29 30 Diff 1′ cot 19.0811 18.9755 8711 7678 6656 18.5645 4645 3655 2677 1708 18.0750 17.9802 8863 7934 7015 17.6106 5205 4314 3432 2558 17.1693 17.0837 16.9990 9150 8319 16.7496 6681 5874 5075 4283 16.3499 2722 1952 1190 16.0435 15.9687 8945 8211 7483 6762 15.6048 5340 4638 3943 3254 15.2571 1893 1222 15.0557 14.9898 14.9244 8596 7954 7317 6685 14.6059 5438 4823 4212 3607 14.3007 tan Diff 1′ 1056 1045 1033 1022 1011 1000 989 979 968 958 948 938 929 919 910 900 891 882 873 865 856 848 839 831 823 815 807 799 792 784 777 769 762 755 748 741 734 728 721 714 708 702 695 689 683 677 671 665 659 654 648 642 637 631 626 621 616 610 605 600 Diff 1′ sec 1.00137 00139 00140 00142 00143 1.00145 00147 00148 00150 00151 1.00153 00155 00156 00158 00159 1.00161 00163 00164 00166 00168 1.00169 00171 00173 00175 00176 1.00178 00180 00182 00183 00185 1.00187 00189 00190 00192 00194 1.00196 00198 00200 00201 00203 1.00205 00207 00209 00211 00213 1.00215 00216 00218 00220 00222 1.00224 00226 00228 00230 00232 1.00234 00236 00238 00240 00242 1.00244 csc Diff 1′ 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 Diff 1′ cos 176° 0.99863 99861 99860 99858 99857 0.99855 99854 99852 99851 99849 0.99847 99846 99844 99842 99841 0.99839 99838 99836 99834 99833 0.99831 99829 99827 99826 99824 0.99822 99821 99819 99817 99815 0.99813 99812 99810 99808 99806 0.99804 99803 99801 99799 99797 0.99795 99793 99792 99790 99788 0.99786 99784 99782 99780 99778 0.99776 99774 99772 99770 99768 0.99766 99764 99762 99760 99758 0.99756 sin Diff 1′ 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 ′ 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 Diff ➙ cos 0.03492 03521 03550 03579 03609 0.03638 03667 03696 03725 03754 0.03783 03812 03842 03871 03900 0.03929 03958 03987 04016 04046 0.04075 04104 04133 04162 04191 0.04220 04250 04279 04308 04337 0.04366 04395 04424 04454 04483 0.04512 04541 04570 04599 04628 0.04658 04687 04716 04745 04774 0.04803 04833 04862 04891 04920 0.04949 04978 05007 05037 05066 0.05095 05124 05153 05182 05212 0.05241 Diff 1′ ➙ 2367 2328 2290 2253 2217 2182 2148 2114 2081 2049 2018 1988 1958 1928 1900 1872 1845 1818 1792 1766 1741 1716 1692 1669 1646 1623 1601 1580 1558 1538 1517 1497 1478 1459 1440 1421 1403 1385 1368 1351 1334 1318 1301 1286 1270 1255 1240 1225 1210 1196 1182 1168 1155 1142 1128 1116 1103 1091 1078 1066 ➙ 28.6537 4170 28.1842 27.9551 7298 27.5080 2898 27.0750 26.8636 6555 26.4505 2487 26.0499 25.8542 6613 25.4713 2841 25.0997 24.9179 7387 24.5621 3880 2164 24.0471 23.8802 23.7156 5533 3932 2352 23.0794 22.9256 7739 6241 4764 3305 22.1865 22.0444 21.9041 7656 6288 21.4937 3603 2285 21.0984 20.9698 20.8428 7174 5934 4709 3499 20.2303 20.1121 19.9952 8798 7656 19.6528 5412 4309 3218 2140 19.1073 cot ➙ 29 29 29 29 29 29 29 30 29 29 29 29 29 29 29 29 29 29 29 29 29 29 30 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 30 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 30 29 Diff 1′ 1′ 86° ➙ 92°➙ 177° ➙ 0.03490 03519 03548 03577 03606 0.03635 03664 03693 03723 03752 0.03781 03810 03839 03868 03897 0.03926 03955 03984 04013 04042 0.04071 04100 04129 04159 04188 0.04217 04246 04275 04304 04333 0.04362 04391 04420 04449 04478 0.04507 04536 04565 04594 04623 0.04653 04682 04711 04740 04769 0.04798 04827 04856 04885 04914 0.04943 04972 05001 05030 05059 0.05088 05117 05146 05175 05205 0.05234 tan ➙ Diff 1′ ➙ csc ➙ ➙ ′ 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 Diff 1′ ➙ 2°➙ sin 576 TABLE Natural Trigonometric Functions TABLE TABLE Natural Trigonometric Functions Natural Trigonometric Functions 1′ sec Diff 1′ cot Diff 1′ 14.3007 2411 1821 1235 0655 14.0079 13.9507 8940 8378 7821 13.7267 6719 6174 5634 5098 13.4566 4039 3515 2996 2480 13.1969 1461 0958 13.0458 12.9962 12.9469 8981 8496 8014 7536 12.7062 6591 6124 5660 5199 12.4742 4288 3838 3390 2946 12.2505 2067 1632 1201 0772 12.0346 11.9923 9504 9087 8673 11.8262 7853 7448 7045 6645 11.6248 5853 5461 5072 4685 11.4301 tan 595 590 586 581 576 571 567 562 558 553 549 544 540 536 532 528 523 519 515 511 508 504 500 496 492 489 485 481 478 474 471 467 464 461 457 454 451 447 444 441 438 435 432 429 426 423 420 417 414 411 408 406 403 400 397 395 392 389 387 384 Diff 1′ 1.00244 00246 00248 00250 00252 1.00254 00257 00259 00261 00263 1.00265 00267 00269 00271 00274 1.00276 00278 00280 00282 00284 1.00287 00289 00291 00293 00296 1.00298 00300 00302 00305 00307 1.00309 00312 00314 00316 00318 1.00321 00323 00326 00328 00330 1.00333 00335 00337 00340 00342 1.00345 00347 00350 00352 00354 1.00357 00359 00362 00364 00367 1.00369 00372 00374 00377 00379 1.00382 csc Diff 1′ 2 2 2 2 2 2 2 2 2 2 2 3 2 2 3 2 3 3 3 Diff 1′ cos 0.99756 99754 99752 99750 99748 0.99746 99744 99742 99740 99738 0.99736 99734 99731 99729 99727 0.99725 99723 99721 99719 99716 0.99714 99712 99710 99708 99705 0.99703 99701 99699 99696 99694 0.99692 99689 99687 99685 99683 0.99680 99678 99676 99673 99671 0.99668 99666 99664 99661 99659 0.99657 99654 99652 99649 99647 0.99644 99642 99639 99637 99635 0.99632 99630 99627 99625 99622 0.99619 sin Diff 1′ 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 3 3 2 3 3 ′ 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 Diff 1′ 85° 5°➙ ′ 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 sin Diff 1′ csc Diff 1′ 0.08716 08745 08774 08803 08831 0.08860 08889 08918 08947 08976 0.09005 09034 09063 09092 09121 0.09150 09179 09208 09237 09266 0.09295 09324 09353 09382 09411 0.09440 09469 09498 09527 09556 0.09585 09614 09642 09671 09700 0.09729 09758 09787 09816 09845 0.09874 09903 09932 09961 09990 0.10019 10048 10077 10106 10135 0.10164 10192 10221 10250 10279 0.10308 10337 10366 10395 10424 0.10453 29 29 29 28 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 28 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 28 29 29 29 29 29 29 29 29 29 11.4737 4357 3979 3604 3231 11.2861 2493 2128 1765 1404 11.1045 0689 11.0336 10.9984 9635 10.9288 8943 8600 8260 7921 10.7585 7251 6919 6589 6261 10.5935 5611 5289 4969 4650 10.4334 4020 3708 3397 3089 10.2782 2477 2174 1873 1573 10.1275 0979 0685 0392 10.0101 9.98123 95248 92389 89547 86722 9.83912 81119 78341 75579 72833 9.70103 67387 64687 62002 59332 9.56677 380 378 375 373 370 368 365 363 361 358 356 354 352 349 347 345 343 341 338 336 334 332 330 328 326 324 322 320 318 316 314 312 310 309 307 305 303 301 300 298 296 294 293 291 2891 2876 2859 2841 2826 2810 2793 2778 2761 2747 2730 2716 2700 2684 2670 2656 ➙ Diff 29 29 29 30 29 29 29 30 29 29 29 30 29 29 29 30 29 29 29 30 29 29 29 30 29 29 29 30 29 29 29 30 29 29 30 29 29 29 30 29 29 29 30 29 29 30 29 29 30 29 29 29 30 29 29 30 29 29 30 29 sec 95°➙ cos Diff 1′ sec Diff 1′ tan 0.08749 08778 08807 08837 08866 0.08895 08925 08954 08983 09013 0.09042 09071 09101 09130 09159 0.09189 09218 09247 09277 09306 0.09335 09365 09394 09423 09453 0.09482 09511 09541 09570 09600 0.09629 09658 09688 09717 09746 0.09776 09805 09834 09864 09893 0.09923 09952 09981 10011 10040 0.10069 10099 10128 10158 10187 0.10216 10246 10275 10305 10334 0.10363 10393 10422 10452 10481 0.10510 cot Diff 1′ 29 29 30 29 29 30 29 29 30 29 29 30 29 29 30 29 29 30 29 29 30 29 29 30 29 29 30 29 30 29 29 30 29 29 30 29 29 30 29 30 29 29 30 29 29 30 29 30 29 29 30 29 30 29 29 30 29 30 29 29 Diff 1′ cot 11.4301 3919 3540 3163 2789 11.2417 2048 1681 1316 0954 11.0594 11.0237 10.9882 9529 9178 10.8829 8483 8139 7797 7457 10.7119 6783 6450 6118 5789 10.5462 5136 4813 4491 4172 10.3854 3538 3224 2913 2602 10.2294 1988 1683 1381 1080 10.0780 0483 10.0187 9.98931 96007 9.93101 90211 87338 84482 81641 9.78817 76009 73217 70441 67680 9.64935 62205 59490 56791 54106 9.51436 tan Diff 1′ 382 379 377 374 372 369 367 365 362 360 358 355 353 351 349 346 344 342 340 338 336 334 332 329 327 325 323 321 320 318 316 314 312 310 308 306 305 303 301 299 297 296 2940 2923 2907 2890 2873 2857 2840 2824 2809 2792 2777 2760 2746 2730 2714 2700 2684 2670 Diff 1′ sec 1.00382 00385 00387 00390 00392 1.00395 00397 00400 00403 00405 1.00408 00411 00413 00416 00419 1.00421 00424 00427 00429 00432 1.00435 00438 00440 00443 00446 1.00449 00451 00454 00457 00460 1.00463 00465 00468 00471 00474 1.00477 00480 00482 00485 00488 1.00491 00494 00497 00500 00503 1.00506 00509 00512 00515 00518 1.00521 00524 00527 00530 00533 1.00536 00539 00542 00545 00548 1.00551 csc Diff 1′ 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 Diff 1′ cos 174° 0.99619 99617 99614 99612 99609 0.99607 99604 99602 99599 99596 0.99594 99591 99588 99586 99583 0.99580 99578 99575 99572 99570 0.99567 99564 99562 99559 99556 0.99553 99551 99548 99545 99542 0.99540 99537 99534 99531 99528 0.99526 99523 99520 99517 99514 0.99511 99508 99506 99503 99500 0.99497 99494 99491 99488 99485 0.99482 99479 99476 99473 99470 0.99467 99464 99461 99458 99455 0.99452 sin Diff 1′ 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 ′ 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 Diff ➙ cos 0.06993 07022 07051 07080 07110 0.07139 07168 07197 07227 07256 0.07285 07314 07344 07373 07402 0.07431 07461 07490 07519 07548 0.07578 07607 07636 07665 07695 0.07724 07753 07782 07812 07841 0.07870 07899 07929 07958 07987 0.08017 08046 08075 08104 08134 0.08163 08192 08221 08251 08280 0.08309 08339 08368 08397 08427 0.08456 08485 08514 08544 08573 0.08602 08632 08661 08690 08720 0.08749 Diff 1′ ➙ 594 589 584 579 575 570 565 561 556 552 547 543 539 534 530 526 522 518 514 510 506 502 498 495 491 487 484 480 476 473 469 466 462 459 456 452 449 446 443 440 436 433 430 427 424 421 418 415 413 410 407 404 401 399 396 393 391 388 385 383 ➙ 14.3356 2762 2173 1589 1010 14.0435 13.9865 9300 8739 8183 13.7631 7084 6541 6002 5468 13.4937 4411 3889 3371 2857 13.2347 1841 1339 0840 13.0346 12.9855 9368 8884 8404 7928 12.7455 6986 6520 6057 5598 12.5142 4690 4241 3795 3352 12.2913 2476 2043 1612 1185 12.0761 12.0340 11.9921 9506 9093 11.8684 8277 7873 7471 7073 11.6677 6284 5893 5505 5120 11.4737 cot ➙ 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 Diff 1′ 1′ 84° ➙ 0.06976 07005 07034 07063 07092 0.07121 07150 07179 07208 07237 0.07266 07295 07324 07353 07382 0.07411 07440 07469 07498 07527 0.07556 07585 07614 07643 07672 0.07701 07730 07759 07788 07817 0.07846 07875 07904 07933 07962 0.07991 08020 08049 08078 08107 0.08136 08165 08194 08223 08252 0.08281 08310 08339 08368 08397 0.08426 08455 08484 08513 08542 0.08571 08600 08629 08658 08687 0.08716 tan 577 94°➙ 175° ➙ Diff 1′ ➙ csc ➙ Diff 1′ ➙ ➙ ′ 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 sin ➙ 4°➙ TABLE Natural Trigonometric Functions 1′ sec Diff 1′ cot Diff 1′ 9.51436 48781 46141 43515 40904 9.38307 35724 33155 30599 28058 9.25530 23016 20516 18028 15554 9.13093 10646 08211 05789 03379 9.00983 8.98598 96227 93867 91520 8.89185 86862 84551 82252 79964 8.77689 75425 73172 70931 68701 8.66482 64275 62078 59893 57718 8.55555 53402 51259 49128 47007 8.44896 42795 40705 38625 36555 8.34496 32446 30406 28376 26355 8.24345 22344 20352 18370 16398 8.14435 tan 2654 2640 2626 2611 2598 2583 2570 2556 2541 2528 2514 2500 2488 2474 2460 2448 2434 2422 2410 2397 2384 2371 2360 2348 2336 2322 2311 2300 2288 2276 2264 2252 2241 2230 2219 2208 2197 2186 2174 2163 2152 2142 2131 2121 2110 2100 2090 2080 2070 2060 2050 2040 2030 2020 2010 2001 1991 1981 1972 1963 Diff 1′ 1.00551 00554 00557 00560 00563 1.00566 00569 00573 00576 00579 1.00582 00585 00588 00592 00595 1.00598 00601 00604 00608 00611 1.00614 00617 00621 00624 00627 1.00630 00634 00637 00640 00644 1.00647 00650 00654 00657 00660 1.00664 00667 00671 00674 00677 1.00681 00684 00688 00691 00695 1.00698 00701 00705 00708 00712 1.00715 00719 00722 00726 00730 1.00733 00737 00740 00744 00747 1.00751 csc Diff 1′ 3 3 3 3 3 3 3 3 3 3 3 3 4 3 4 3 4 4 4 4 Diff 1′ cos 0.99452 99449 99446 99443 99440 0.99437 99434 99431 99428 99424 0.99421 99418 99415 99412 99409 0.99406 99402 99399 99396 99393 0.99390 99386 99383 99380 99377 0.99374 99370 99367 99364 99360 0.99357 99354 99351 99347 99344 0.99341 99337 99334 99331 99327 0.99324 99320 99317 99314 99310 0.99307 99303 99300 99297 99293 0.99290 99286 99283 99279 99276 0.99272 99269 99265 99262 99258 0.99255 sin Diff 1′ 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 3 4 3 4 4 4 ′ 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 Diff 1′ 83° 7°➙ ′ 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 sin Diff 1′ csc Diff 1′ 0.12187 12216 12245 12274 12302 0.12331 12360 12389 12418 12447 0.12476 12504 12533 12562 12591 0.12620 12649 12678 12706 12735 0.12764 12793 12822 12851 12880 0.12908 12937 12966 12995 13024 0.13053 13081 13110 13139 13168 0.13197 13226 13254 13283 13312 0.13341 13370 13399 13427 13456 0.13485 13514 13543 13572 13600 0.13629 13658 13687 13716 13744 0.13773 13802 13831 13860 13889 0.13917 29 29 29 28 29 29 29 29 29 29 28 29 29 29 29 29 29 28 29 29 29 29 29 29 28 29 29 29 29 29 28 29 29 29 29 29 28 29 29 29 29 29 28 29 29 29 29 29 28 29 29 29 29 28 29 29 29 29 29 28 8.20551 18612 16681 14760 12849 8.10946 09052 07167 05291 03423 8.01565 7.99714 97873 96040 94216 7.92399 90592 88792 87001 85218 7.83443 81677 79918 78167 76424 7.74689 72962 71242 69530 67826 7.66130 64441 62759 61085 59418 7.57759 56107 54462 52825 51194 7.49571 47955 46346 44743 43148 7.41560 39978 38403 36835 35274 7.33719 32171 30630 29095 27566 7.26044 24529 23019 21517 20020 7.18530 1940 1930 1920 1911 1902 1893 1886 1877 1868 1859 1850 1841 1832 1824 1817 1808 1800 1791 1782 1774 1767 1759 1750 1742 1736 1728 1720 1711 1704 1697 1690 1681 1674 1667 1660 1652 1644 1638 1630 1623 1617 1610 1602 1596 1589 1581 1574 1569 1561 1554 1549 1541 1534 1529 1521 1516 1510 1502 1497 1490 ➙ Diff 30 29 30 29 29 30 29 30 29 30 29 29 30 29 30 29 30 29 30 29 29 30 29 30 29 30 29 30 29 30 29 29 30 29 30 29 30 29 30 29 30 29 30 29 30 29 30 29 30 29 30 29 30 29 30 29 30 29 30 29 sec 97°➙ cos Diff 1′ sec Diff 1′ tan 0.12278 12308 12338 12367 12397 0.12426 12456 12485 12515 12544 0.12574 12603 12633 12662 12692 0.12722 12751 12781 12810 12840 0.12869 12899 12929 12958 12988 0.13017 13047 13076 13106 13136 0.13165 13195 13224 13254 13284 0.13313 13343 13372 13402 13432 0.13461 13491 13521 13550 13580 0.13609 13639 13669 13698 13728 0.13758 13787 13817 13846 13876 0.13906 13935 13965 13995 14024 0.14054 cot Diff 1′ 30 30 29 30 29 30 29 30 29 30 29 30 29 30 30 29 30 29 30 29 30 30 29 30 29 30 29 30 30 29 30 29 30 30 29 30 29 30 30 29 30 30 29 30 29 30 30 29 30 30 29 30 29 30 30 29 30 30 29 30 Diff 1′ cot 8.14435 12481 10536 08600 06674 8.04756 02848 8.00948 7.99058 97176 7.95302 93438 91582 89734 87895 7.86064 84242 82428 80622 78825 7.77035 75254 73480 71715 69957 7.68208 66466 64732 63005 61287 7.59575 57872 56176 54487 52806 7.51132 49465 47806 46154 44509 7.42871 41240 39616 37999 36389 7.34786 33190 31600 30018 28442 7.26873 25310 23754 22204 20661 7.19125 17594 16071 14553 13042 7.11537 tan Diff 1′ 1953 1944 1936 1927 1918 1909 1900 1890 1882 1873 1864 1857 1848 1840 1830 1822 1814 1806 1798 1790 1781 1773 1766 1758 1750 1741 1734 1727 1719 1711 1703 1697 1689 1681 1673 1667 1660 1652 1646 1638 1630 1623 1617 1610 1603 1597 1590 1582 1576 1570 1562 1557 1550 1543 1537 1530 1523 1518 1511 1504 Diff 1′ sec 1.00751 00755 00758 00762 00765 1.00769 00773 00776 00780 00784 1.00787 00791 00795 00799 00802 1.00806 00810 00813 00817 00821 1.00825 00828 00832 00836 00840 1.00844 00848 00851 00855 00859 1.00863 00867 00871 00875 00878 1.00882 00886 00890 00894 00898 1.00902 00906 00910 00914 00918 1.00922 00926 00930 00934 00938 1.00942 00946 00950 00954 00958 1.00962 00966 00970 00975 00979 1.00983 csc Diff 1′ 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 Diff 1′ cos 172° 0.99255 99251 99248 99244 99240 0.99237 99233 99230 99226 99222 0.99219 99215 99211 99208 99204 0.99200 99197 99193 99189 99186 0.99182 99178 99175 99171 99167 0.99163 99160 99156 99152 99148 0.99144 99141 99137 99133 99129 0.99125 99122 99118 99114 99110 0.99106 99102 99098 99094 99091 0.99087 99083 99079 99075 99071 0.99067 99063 99059 99055 99051 0.99047 99043 99039 99035 99031 0.99027 sin Diff 1′ 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 ′ 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 Diff ➙ cos 0.10510 10540 10569 10599 10628 0.10657 10687 10716 10746 10775 0.10805 10834 10863 10893 10922 0.10952 10981 11011 11040 11070 0.11099 11128 11158 11187 11217 0.11246 11276 11305 11335 11364 0.11394 11423 11452 11482 11511 0.11541 11570 11600 11629 11659 0.11688 11718 11747 11777 11806 0.11836 11865 11895 11924 11954 0.11983 12013 12042 12072 12101 0.12131 12160 12190 12219 12249 0.12278 Diff 1′ ➙ 2640 2626 2611 2597 2582 2569 2554 2540 2527 2513 2500 2487 2472 2460 2447 2433 2420 2408 2394 2382 2370 2358 2344 2332 2320 2309 2297 2284 2272 2261 2250 2239 2227 2216 2204 2192 2181 2170 2160 2150 2139 2128 2118 2107 2097 2086 2076 2066 2056 2046 2036 2026 2016 2006 1997 1987 1977 1968 1958 1949 ➙ 9.56677 54037 51411 48800 46203 9.43620 41052 38497 35957 33430 9.30917 28417 25931 23459 20999 9.18553 16120 13699 11292 08897 9.06515 04146 9.01788 8.99444 97111 8.94791 92482 90186 87901 85628 8.83367 81118 78880 76653 74438 8.72234 70041 67859 65688 63528 8.61379 59241 57113 54996 52889 8.50793 48707 46632 44566 42511 8.40466 38431 36405 34390 32384 8.30388 28402 26425 24457 22500 8.20551 cot ➙ 29 29 29 29 28 29 29 29 29 29 29 29 29 29 29 29 29 28 29 29 29 29 29 29 29 29 29 29 28 29 29 29 29 29 29 29 29 29 28 29 29 29 29 29 29 29 29 28 29 29 29 29 29 29 29 28 29 29 29 29 Diff 1′ 1′ 82° ➙ 96°➙ 173° ➙ 0.10453 10482 10511 10540 10569 0.10597 10626 10655 10684 10713 0.10742 10771 10800 10829 10858 0.10887 10916 10945 10973 11002 0.11031 11060 11089 11118 11147 0.11176 11205 11234 11263 11291 0.11320 11349 11378 11407 11436 0.11465 11494 11523 11552 11580 0.11609 11638 11667 11696 11725 0.11754 11783 11812 11840 11869 0.11898 11927 11956 11985 12014 0.12043 12071 12100 12129 12158 0.12187 tan ➙ Diff 1′ ➙ csc ➙ ➙ ′ 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 Diff 1′ ➙ 6°➙ sin 578 TABLE Natural Trigonometric Functions TABLE TABLE Natural Trigonometric Functions Natural Trigonometric Functions 1′ sec Diff 1′ cot Diff 1′ 1.19175 19105 19035 18964 18894 1.18824 18754 18684 18614 18544 1.18474 18404 18334 18264 18194 1.18125 18055 17986 17916 17846 1.17777 17708 17638 17569 17500 1.17430 17361 17292 17223 17154 1.17085 17016 16947 16878 16809 1.16741 16672 16603 16535 16466 1.16398 16329 16261 16192 16124 1.16056 15987 15919 15851 15783 1.15715 15647 15579 15511 15443 1.15375 15308 15240 15172 15104 1.15037 tan 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 69 69 69 69 69 69 69 69 69 69 69 69 69 69 69 69 69 69 69 69 69 69 68 68 68 68 68 68 68 68 68 Diff 1′ 1.30541 30573 30605 30636 30668 1.30700 30732 30764 30796 30829 1.30861 30893 30925 30957 30989 1.31022 31054 31086 31119 31151 1.31183 31216 31248 31281 31313 1.31346 31378 31411 31443 31476 1.31509 31541 31574 31607 31640 1.31672 31705 31738 31771 31804 1.31837 31870 31903 31936 31969 1.32002 32035 32068 32101 32134 1.32168 32201 32234 32267 32301 1.32334 32368 32401 32434 32468 1.32501 csc Diff 1′ 32 32 31 32 32 32 32 32 33 32 32 32 32 32 33 32 32 33 32 32 33 32 33 32 33 32 33 32 33 33 32 33 33 33 32 33 33 33 33 33 33 33 33 33 33 33 33 33 33 34 33 33 33 34 33 34 33 33 34 33 Diff 1′ cos 0.76604 76586 76567 76548 76530 0.76511 76492 76473 76455 76436 0.76417 76398 76380 76361 76342 0.76323 76304 76286 76267 76248 0.76229 76210 76192 76173 76154 0.76135 76116 76097 76078 76059 0.76041 76022 76003 75984 75965 0.75946 75927 75908 75889 75870 0.75851 75832 75813 75794 75775 0.75756 75738 75719 75700 75680 0.75661 75642 75623 75604 75585 0.75566 75547 75528 75509 75490 0.75471 sin Diff 1′ 18 19 19 18 19 19 19 18 19 19 19 18 19 19 19 19 18 19 19 19 19 18 19 19 19 19 19 19 19 18 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 18 19 19 20 19 19 19 19 19 19 19 19 19 19 19 ′ 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 Diff 1′ 49° 41°➙ ′ 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 sin Diff 1′ csc Diff 1′ 0.65606 65628 65650 65672 65694 0.65716 65738 65759 65781 65803 0.65825 65847 65869 65891 65913 0.65935 65956 65978 66000 66022 0.66044 66066 66088 66109 66131 0.66153 66175 66197 66218 66240 0.66262 66284 66306 66327 66349 0.66371 66393 66414 66436 66458 0.66480 66501 66523 66545 66566 0.66588 66610 66632 66653 66675 0.66697 66718 66740 66762 66783 0.66805 66827 66848 66870 66891 0.66913 22 22 22 22 22 22 21 22 22 22 22 22 22 22 22 21 22 22 22 22 22 22 21 22 22 22 22 21 22 22 22 22 21 22 22 22 21 22 22 22 21 22 22 21 22 22 22 21 22 22 21 22 22 21 22 22 21 22 21 22 1.52425 52374 52323 52273 52222 1.52171 52120 52069 52019 51968 1.51918 51867 51817 51766 51716 1.51665 51615 51565 51515 51465 1.51415 51364 51314 51265 51215 1.51165 51115 51065 51015 50966 1.50916 50866 50817 50767 50718 1.50669 50619 50570 50521 50471 1.50422 50373 50324 50275 50226 1.50177 50128 50079 50030 49981 1.49933 49884 49835 49787 49738 1.49690 49641 49593 49544 49496 1.49448 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 ➙ Diff 50 49 50 49 50 50 50 49 50 50 50 50 49 50 50 50 50 50 50 50 50 50 51 50 50 50 50 51 50 50 50 51 50 50 51 50 51 50 51 50 51 51 50 51 51 50 51 51 50 51 51 51 51 51 51 51 51 51 51 51 sec 131°➙ cos Diff 1′ sec Diff 1′ tan 0.86929 86980 87031 87082 87133 0.87184 87236 87287 87338 87389 0.87441 87492 87543 87595 87646 0.87698 87749 87801 87852 87904 0.87955 88007 88059 88110 88162 0.88214 88265 88317 88369 88421 0.88473 88524 88576 88628 88680 0.88732 88784 88836 88888 88940 0.88992 89045 89097 89149 89201 0.89253 89306 89358 89410 89463 0.89515 89567 89620 89672 89725 0.89777 89830 89883 89935 89988 0.90040 cot Diff 1′ 51 51 51 51 51 52 51 51 51 52 51 51 52 51 52 51 52 51 52 51 52 52 51 52 52 51 52 52 52 52 51 52 52 52 52 52 52 52 52 52 53 52 52 52 52 53 52 52 53 52 52 53 52 53 52 53 53 52 53 52 Diff 1′ cot 1.15037 14969 14902 14834 14767 1.14699 14632 14565 14498 14430 1.14363 14296 14229 14162 14095 1.14028 13961 13894 13828 13761 1.13694 13627 13561 13494 13428 1.13361 13295 13228 13162 13096 1.13029 12963 12897 12831 12765 1.12699 12633 12567 12501 12435 1.12369 12303 12238 12172 12106 1.12041 11975 11909 11844 11778 1.11713 11648 11582 11517 11452 1.11387 11321 11256 11191 11126 1.11061 tan Diff 1′ 68 68 68 68 68 68 68 68 68 68 68 68 68 67 67 67 67 67 67 67 67 67 67 67 67 67 67 67 67 67 67 67 67 67 67 67 66 66 66 66 66 66 66 66 66 66 66 66 66 66 66 66 66 66 66 66 66 66 66 64 Diff 1′ sec 1.32501 32535 32568 32602 32636 1.32669 32703 32737 32770 32804 1.32838 32872 32905 32939 32973 1.33007 33041 33075 33109 33143 1.33177 33211 33245 33279 33314 1.33348 33382 33416 33451 33485 1.33519 33554 33588 33622 33657 1.33691 33726 33760 33795 33830 1.33864 33899 33934 33968 34003 1.34038 34073 34108 34142 34177 1.34212 34247 34282 34317 34352 1.34387 34423 34458 34493 34528 1.34563 csc Diff 1′ 34 33 34 34 33 34 34 33 34 34 34 33 34 34 34 34 34 34 34 34 34 34 34 35 34 34 34 35 34 34 35 34 34 35 34 35 34 35 35 34 35 35 34 35 35 35 35 34 35 35 35 35 35 35 35 36 35 35 35 35 Diff 1′ cos 138° 0.75471 75452 75433 75414 75395 0.75375 75356 75337 75318 75299 0.75280 75261 75241 75222 75203 0.75184 75165 75146 75126 75107 0.75088 75069 75050 75030 75011 0.74992 74973 74953 74934 74915 0.74896 74876 74857 74838 74818 0.74799 74780 74760 74741 74722 0.74703 74683 74664 74644 74625 0.74606 74586 74567 74548 74528 0.74509 74489 74470 74451 74431 0.74412 74392 74373 74353 74334 0.74314 sin Diff 1′ 19 19 19 19 20 19 19 19 19 19 19 20 19 19 19 19 19 20 19 19 19 19 20 19 19 19 20 19 19 19 20 19 19 20 19 19 20 19 19 19 20 19 20 19 19 20 19 19 20 19 20 19 19 20 19 20 19 20 19 20 ′ 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 Diff ➙ cos 0.83910 83960 84009 84059 84108 0.84158 84208 84258 84307 84357 0.84407 84457 84507 84556 84606 0.84656 84706 84756 84806 84856 0.84906 84956 85006 85057 85107 0.85157 85207 85257 85308 85358 0.85408 85458 85509 85559 85609 0.85660 85710 85761 85811 85862 0.85912 85963 86014 86064 86115 0.86166 86216 86267 86318 86368 0.86419 86470 86521 86572 86623 0.86674 86725 86776 86827 86878 0.86929 Diff 1′ ➙ 53 53 53 53 53 53 53 53 53 53 53 53 53 53 53 53 53 53 53 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 52 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51 ➙ 1.55572 55518 55465 55411 55357 1.55303 55250 55196 55143 55089 1.55036 54982 54929 54876 54822 1.54769 54716 54663 54610 54557 1.54504 54451 54398 54345 54292 1.54240 54187 54134 54082 54029 1.53977 53924 53872 53820 53768 1.53715 53663 53611 53559 53507 1.53455 53403 53351 53299 53247 1.53196 53144 53092 53041 52989 1.52938 52886 52835 52784 52732 1.52681 52630 52579 52527 52476 1.52425 cot ➙ 22 22 23 22 22 22 23 22 22 22 23 22 22 22 22 23 22 22 22 22 23 22 22 22 22 22 22 23 22 22 22 22 22 22 22 22 23 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 Diff 1′ 1′ 48° ➙ 0.64279 64301 64323 64346 64368 0.64390 64412 64435 64457 64479 0.64501 64524 64546 64568 64590 0.64612 64635 64657 64679 64701 0.64723 64746 64768 64790 64812 0.64834 64856 64878 64901 64923 0.64945 64967 64989 65011 65033 0.65055 65077 65100 65122 65144 0.65166 65188 65210 65232 65254 0.65276 65298 65320 65342 65364 0.65386 65408 65430 65452 65474 0.65496 65518 65540 65562 65584 0.65606 tan 595 130°➙ 139° ➙ Diff 1′ ➙ csc ➙ Diff 1′ ➙ ➙ ′ 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 sin ➙ 40°➙ TABLE Natural Trigonometric Functions 1′ sec Diff 1′ cot Diff 1′ 1.11061 10996 10931 10867 10802 1.10737 10672 10607 10543 10478 1.10414 10349 10285 10220 10156 1.10091 10027 09963 09899 09834 1.09770 09706 09642 09578 09514 1.09450 09386 09322 09258 09195 1.09131 09067 09003 08940 08876 1.08813 08749 08686 08622 08559 1.08496 08432 08369 08306 08243 1.08179 08116 08053 07990 07927 1.07864 07801 07738 07676 07613 1.07550 07487 07425 07362 07299 1.07237 tan 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 64 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 62 62 62 62 62 62 62 62 62 62 62 62 Diff 1′ 1.34563 34599 34634 34669 34704 1.34740 34775 34811 34846 34882 1.34917 34953 34988 35024 35060 1.35095 35131 35167 35203 35238 1.35274 35310 35346 35382 35418 1.35454 35490 35526 35562 35598 1.35634 35670 35707 35743 35779 1.35815 35852 35888 35924 35961 1.35997 36034 36070 36107 36143 1.36180 36217 36253 36290 36327 1.36363 36400 36437 36474 36511 1.36548 36585 36622 36659 36696 1.36733 csc Diff 1′ 36 35 35 35 36 35 36 35 36 35 36 35 36 36 35 36 36 36 35 36 36 36 36 36 36 36 36 36 36 36 36 37 36 36 36 37 36 36 37 36 37 36 37 36 37 37 36 37 37 36 37 37 37 37 37 37 37 37 37 37 Diff 1′ cos 0.74314 74295 74276 74256 74237 0.74217 74198 74178 74159 74139 0.74120 74100 74080 74061 74041 0.74022 74002 73983 73963 73944 0.73924 73904 73885 73865 73846 0.73826 73806 73787 73767 73747 0.73728 73708 73688 73669 73649 0.73629 73610 73590 73570 73551 0.73531 73511 73491 73472 73452 0.73432 73413 73393 73373 73353 0.73333 73314 73294 73274 73254 0.73234 73215 73195 73175 73155 0.73135 sin Diff 1′ 19 19 20 19 20 19 20 19 20 19 20 20 19 20 19 20 19 20 19 20 20 19 20 19 20 20 19 20 20 19 20 20 19 20 20 19 20 20 19 20 20 20 19 20 20 19 20 20 20 20 19 20 20 20 20 19 20 20 20 20 ′ 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 Diff 1′ 47° 43°➙ ′ 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 sin Diff 1′ csc Diff 1′ 0.68200 68221 68242 68264 68285 0.68306 68327 68349 68370 68391 0.68412 68434 68455 68476 68497 0.68518 68539 68561 68582 68603 0.68624 68645 68666 68688 68709 0.68730 68751 68772 68793 68814 0.68835 68857 68878 68899 68920 0.68941 68962 68983 69004 69025 0.69046 69067 69088 69109 69130 0.69151 69172 69193 69214 69235 0.69256 69277 69298 69319 69340 0.69361 69382 69403 69424 69445 0.69466 21 21 22 21 21 21 22 21 21 21 22 21 21 21 21 21 22 21 21 21 21 21 22 21 21 21 21 21 21 21 22 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 1.46628 46582 46537 46491 46445 1.46400 46354 46309 46263 46218 1.46173 46127 46082 46037 45992 1.45946 45901 45856 45811 45766 1.45721 45676 45631 45587 45542 1.45497 45452 45408 45363 45319 1.45274 45229 45185 45141 45096 1.45052 45007 44963 44919 44875 1.44831 44787 44742 44698 44654 1.44610 44567 44523 44479 44435 1.44391 44347 44304 44260 44217 1.44173 44129 44086 44042 43999 1.43956 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 44 44 44 44 44 44 44 44 44 44 44 44 44 44 44 44 44 44 44 44 44 44 44 44 44 44 43 43 43 43 43 43 43 43 43 43 43 43 43 43 43 43 ➙ Diff 53 53 53 52 53 53 53 53 53 53 52 53 53 54 53 53 53 53 53 53 54 53 53 54 53 53 54 53 54 53 54 53 54 53 54 54 53 54 54 54 54 53 54 54 54 54 54 54 54 54 54 54 55 54 54 54 54 55 54 55 sec 133°➙ cos Diff 1′ sec Diff 1′ tan 0.93252 93306 93360 93415 93469 0.93524 93578 93633 93688 93742 0.93797 93852 93906 93961 94016 0.94071 94125 94180 94235 94290 0.94345 94400 94455 94510 94565 0.94620 94676 94731 94786 94841 0.94896 94952 95007 95062 95118 0.95173 95229 95284 95340 95395 0.95451 95506 95562 95618 95673 0.95729 95785 95841 95897 95952 0.96008 96064 96120 96176 96232 0.96288 96344 96400 96457 96513 0.96569 cot Diff 1′ 54 54 55 54 55 54 55 55 54 55 55 54 55 55 55 54 55 55 55 55 55 55 55 55 55 56 55 55 55 55 56 55 55 56 55 56 55 56 55 56 55 56 56 55 56 56 56 56 55 56 56 56 56 56 56 56 56 57 56 56 Diff 1′ cot 1.07237 07174 07112 07049 06987 1.06925 06862 06800 06738 06676 1.06613 06551 06489 06427 06365 1.06303 06241 06179 06117 06056 1.05994 05932 05870 05809 05747 1.05685 05624 05562 05501 05439 1.05378 05317 05255 05194 05133 1.05072 05010 04949 04888 04827 1.04766 04705 04644 04583 04522 1.04461 04401 04340 04279 04218 1.04158 04097 04036 03976 03915 1.03855 03794 03734 03674 03613 1.03553 tan Diff 1′ 62 62 62 62 62 62 62 62 62 62 62 62 62 62 61 61 61 61 61 61 61 61 61 61 61 61 61 61 61 61 61 61 61 61 61 61 61 61 61 61 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 Diff 1′ sec 1.36733 36770 36807 36844 36881 1.36919 36956 36993 37030 37068 1.37105 37143 37180 37218 37255 1.37293 37330 37368 37406 37443 1.37481 37519 37556 37594 37632 1.37670 37708 37746 37784 37822 1.37860 37898 37936 37974 38012 1.38051 38089 38127 38165 38204 1.38242 38280 38319 38357 38396 1.38434 38473 38512 38550 38589 1.38628 38666 38705 38744 38783 1.38822 38860 38899 38938 38977 1.39016 csc Diff 1′ 37 37 37 37 38 37 37 37 38 37 38 37 38 37 38 37 38 38 37 38 38 37 38 38 38 38 38 38 38 38 38 38 38 38 39 38 38 38 39 38 38 39 38 39 38 39 39 38 39 39 38 39 39 39 39 38 39 39 39 39 Diff 1′ cos 136° 0.73135 73116 73096 73076 73056 0.73036 73016 72996 72976 72957 0.72937 72917 72897 72877 72857 0.72837 72817 72797 72777 72757 0.72737 72717 72697 72677 72657 0.72637 72617 72597 72577 72557 0.72537 72517 72497 72477 72457 0.72437 72417 72397 72377 72357 0.72337 72317 72297 72277 72257 0.72236 72216 72196 72176 72156 0.72136 72116 72095 72075 72055 0.72035 72015 71995 71974 71954 0.71934 sin Diff 1′ 19 20 20 20 20 20 20 20 19 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 21 20 20 20 20 20 20 21 20 20 20 20 20 21 20 20 ′ 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 Diff ➙ cos 0.90040 90093 90146 90199 90251 0.90304 90357 90410 90463 90516 0.90569 90621 90674 90727 90781 0.90834 90887 90940 90993 91046 0.91099 91153 91206 91259 91313 0.91366 91419 91473 91526 91580 0.91633 91687 91740 91794 91847 0.91901 91955 92008 92062 92116 0.92170 92224 92277 92331 92385 0.92439 92493 92547 92601 92655 0.92709 92763 92817 92872 92926 0.92980 93034 93088 93143 93197 0.93252 Diff 1′ ➙ 49 49 49 49 49 49 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 46 46 46 46 46 46 ➙ 1.49448 49399 49351 49303 49255 1.49207 49159 49111 49063 49015 1.48967 48919 48871 48824 48776 1.48728 48681 48633 48586 48538 1.48491 48443 48396 48349 48301 1.48254 48207 48160 48113 48066 1.48019 47972 47925 47878 47831 1.47784 47738 47691 47644 47598 1.47551 47504 47458 47411 47365 1.47319 47272 47226 47180 47134 1.47087 47041 46995 46949 46903 1.46857 46811 46765 46719 46674 1.46628 cot ➙ 22 21 22 21 22 22 21 22 21 22 22 21 22 21 22 21 22 21 22 21 22 21 22 21 22 21 22 21 22 21 21 22 21 22 21 22 21 21 22 21 22 21 21 22 21 21 22 21 21 22 21 21 22 21 21 22 21 21 22 21 Diff 1′ 1′ 46° ➙ 132°➙ 137° ➙ 0.66913 66935 66956 66978 66999 0.67021 67043 67064 67086 67107 0.67129 67151 67172 67194 67215 0.67237 67258 67280 67301 67323 0.67344 67366 67387 67409 67430 0.67452 67473 67495 67516 67538 0.67559 67580 67602 67623 67645 0.67666 67688 67709 67730 67752 0.67773 67795 67816 67837 67859 0.67880 67901 67923 67944 67965 0.67987 68008 68029 68051 68072 0.68093 68115 68136 68157 68179 0.68200 tan ➙ Diff 1′ ➙ csc ➙ ➙ ′ 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 Diff 1′ ➙ 42°➙ sin 596 TABLE Natural Trigonometric Functions TABLE TABLE Natural Trigonometric Functions Natural Trigonometric Functions 1′ sec Diff 1′ cot Diff 1′ 1.37638 37554 37470 37386 37302 1.37218 37134 37050 36967 36883 1.36800 36716 36633 36549 36466 1.36383 36300 36217 36134 36051 1.35968 35885 35802 35719 35637 1.35554 35472 35389 35307 35224 1.35142 35060 34978 34896 34814 1.34732 34650 34568 34487 34405 1.34323 34242 34160 34079 33998 1.33916 33835 33754 33673 33592 1.33511 33430 33349 33268 33187 1.33107 33026 32946 32865 32785 1.32704 tan 84 84 84 83 83 83 83 83 83 83 83 83 83 83 83 83 83 83 82 82 82 82 82 82 82 82 82 82 82 82 82 82 82 81 81 81 81 81 81 81 81 81 81 81 81 81 81 81 81 80 80 80 80 80 80 80 80 80 80 80 Diff 1′ 1.23607 23633 23659 23685 23711 1.23738 23764 23790 23816 23843 1.23869 23895 23922 23948 23975 1.24001 24028 24054 24081 24107 1.24134 24160 24187 24213 24240 1.24267 24293 24320 24347 24373 1.24400 24427 24454 24481 24508 1.24534 24561 24588 24615 24642 1.24669 24696 24723 24750 24777 1.24804 24832 24859 24886 24913 1.24940 24967 24995 25022 25049 1.25077 25104 25131 25159 25186 1.25214 csc Diff 1′ 26 26 26 26 27 26 26 26 27 26 26 27 26 27 26 27 26 27 26 27 26 27 26 27 27 26 27 27 26 27 27 27 27 27 26 27 27 27 27 27 27 27 27 27 27 28 27 27 27 27 27 28 27 27 28 27 27 28 27 28 Diff 1′ cos 0.80902 80885 80867 80850 80833 0.80816 80799 80782 80765 80748 0.80730 80713 80696 80679 80662 0.80644 80627 80610 80593 80576 0.80558 80541 80524 80507 80489 0.80472 80455 80438 80420 80403 0.80386 80368 80351 80334 80316 0.80299 80282 80264 80247 80230 0.80212 80195 80178 80160 80143 0.80125 80108 80091 80073 80056 0.80038 80021 80003 79986 79968 0.79951 79934 79916 79899 79881 0.79864 sin Diff 1′ 17 18 17 17 17 17 17 17 17 18 17 17 17 17 18 17 17 17 17 18 17 17 17 18 17 17 17 18 17 17 18 17 17 18 17 17 18 17 17 18 17 17 18 17 18 17 17 18 17 18 17 18 17 18 17 17 18 17 18 17 ′ 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 Diff 1′ 53° 37°➙ ′ 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 sin Diff 1′ csc Diff 1′ 0.60182 60205 60228 60251 60274 0.60298 60321 60344 60367 60390 0.60414 60437 60460 60483 60506 0.60529 60553 60576 60599 60622 0.60645 60668 60691 60714 60738 0.60761 60784 60807 60830 60853 0.60876 60899 60922 60945 60968 0.60991 61015 61038 61061 61084 0.61107 61130 61153 61176 61199 0.61222 61245 61268 61291 61314 0.61337 61360 61383 61406 61429 0.61451 61474 61497 61520 61543 0.61566 23 23 23 23 24 23 23 23 23 24 23 23 23 23 23 24 23 23 23 23 23 23 23 24 23 23 23 23 23 23 23 23 23 23 23 24 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 22 23 23 23 23 23 1.66164 66100 66036 65972 65908 1.65844 65780 65717 65653 65589 1.65526 65462 65399 65335 65272 1.65209 65146 65083 65020 64957 1.64894 64831 64768 64705 64643 1.64580 64518 64455 64393 64330 1.64268 64206 64144 64081 64019 1.63957 63895 63834 63772 63710 1.63648 63587 63525 63464 63402 1.63341 63279 63218 63157 63096 1.63035 62974 62913 62852 62791 1.62730 62669 62609 62548 62487 1.62427 64 64 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 62 62 62 62 62 62 62 62 62 62 62 62 62 62 62 62 61 61 61 61 61 61 61 61 61 61 61 61 61 61 61 61 61 60 60 60 60 60 60 60 60 60 ➙ Diff 45 44 45 44 45 44 45 44 45 45 44 45 45 44 45 45 45 44 45 45 45 45 44 45 45 45 45 45 45 45 45 45 45 45 45 46 45 45 45 45 45 46 45 45 46 45 45 46 45 45 46 45 46 45 46 45 46 45 46 45 sec 127°➙ cos Diff 1′ sec Diff 1′ tan 0.75355 75401 75447 75492 75538 0.75584 75629 75675 75721 75767 0.75812 75858 75904 75950 75996 0.76042 76088 76134 76180 76226 0.76272 76318 76364 76410 76456 0.76502 76548 76594 76640 76686 0.76733 76779 76825 76871 76918 0.76964 77010 77057 77103 77149 0.77196 77242 77289 77335 77382 0.77428 77475 77521 77568 77615 0.77661 77708 77754 77801 77848 0.77895 77941 77988 78035 78082 0.78129 cot Diff 1′ 46 46 45 46 46 45 46 46 46 45 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 47 46 46 46 47 46 46 47 46 46 47 46 47 46 47 46 47 46 47 47 46 47 46 47 47 47 46 47 47 47 47 Diff 1′ cot 1.32704 32624 32544 32464 32384 1.32304 32224 32144 32064 31984 1.31904 31825 31745 31666 31586 1.31507 31427 31348 31269 31190 1.31110 31031 30952 30873 30795 1.30716 30637 30558 30480 30401 1.30323 30244 30166 30087 30009 1.29931 29853 29775 29696 29618 1.29541 29463 29385 29307 29229 1.29152 29074 28997 28919 28842 1.28764 28687 28610 28533 28456 1.28379 28302 28225 28148 28071 1.27994 tan Diff 1′ 80 80 80 80 80 80 80 80 80 80 80 80 80 80 80 80 80 80 80 80 80 80 79 79 79 79 79 79 79 79 79 79 79 79 79 79 79 79 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 78 77 77 77 77 Diff 1′ sec 1.25214 25241 25269 25296 25324 1.25351 25379 25406 25434 25462 1.25489 25517 25545 25572 25600 1.25628 25656 25683 25711 25739 1.25767 25795 25823 25851 25879 1.25907 25935 25963 25991 26019 1.26047 26075 26104 26132 26160 1.26188 26216 26245 26273 26301 1.26330 26358 26387 26415 26443 1.26472 26500 26529 26557 26586 1.26615 26643 26672 26701 26729 1.26758 26787 26815 26844 26873 1.26902 csc Diff 1′ 27 28 27 28 27 28 27 28 28 27 28 28 27 28 28 28 27 28 28 28 28 28 28 28 28 28 28 28 28 28 28 29 28 28 28 28 29 28 28 29 28 29 28 28 29 28 29 28 29 29 28 29 29 28 29 29 28 29 29 29 Diff 1′ cos 142° 0.79864 79846 79829 79811 79793 0.79776 79758 79741 79723 79706 0.79688 79671 79653 79635 79618 0.79600 79583 79565 79547 79530 0.79512 79494 79477 79459 79441 0.79424 79406 79388 79371 79353 0.79335 79318 79300 79282 79264 0.79247 79229 79211 79193 79176 0.79158 79140 79122 79105 79087 0.79069 79051 79033 79016 78998 0.78980 78962 78944 78926 78908 0.78891 78873 78855 78837 78819 0.78801 sin Diff 1′ 18 17 18 18 17 18 17 18 17 18 17 18 18 17 18 17 18 18 17 18 18 17 18 18 17 18 18 17 18 18 17 18 18 18 17 18 18 18 17 18 18 18 17 18 18 18 18 17 18 18 18 18 18 18 17 18 18 18 18 18 ′ 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 Diff ➙ cos 0.72654 72699 72743 72788 72832 0.72877 72921 72966 73010 73055 0.73100 73144 73189 73234 73278 0.73323 73368 73413 73457 73502 0.73547 73592 73637 73681 73726 0.73771 73816 73861 73906 73951 0.73996 74041 74086 74131 74176 0.74221 74267 74312 74357 74402 0.74447 74492 74538 74583 74628 0.74674 74719 74764 74810 74855 0.74900 74946 74991 75037 75082 0.75128 75173 75219 75264 75310 0.75355 Diff 1′ ➙ 69 69 68 68 68 68 68 68 68 68 68 68 68 68 68 68 67 67 67 67 67 67 67 67 67 67 67 67 67 67 67 66 66 66 66 66 66 66 66 66 66 66 66 66 66 66 66 64 64 64 64 64 64 64 64 64 64 64 64 64 ➙ 1.70130 70062 69994 69926 69858 1.69790 69723 69655 69587 69520 1.69452 69385 69318 69250 69183 1.69116 69049 68982 68915 68848 1.68782 68715 68648 68582 68515 1.68449 68382 68316 68250 68183 1.68117 68051 67985 67919 67853 1.67788 67722 67656 67591 67525 1.67460 67394 67329 67264 67198 1.67133 67068 67003 66938 66873 1.66809 66744 66679 66615 66550 1.66486 66421 66357 66292 66228 1.66164 cot ➙ 23 24 23 24 23 24 23 24 23 24 23 24 23 24 23 23 24 23 24 23 24 23 23 24 23 24 23 24 23 23 24 23 23 24 23 23 24 23 24 23 23 24 23 23 23 24 23 23 24 23 23 23 24 23 23 24 23 23 23 24 Diff 1′ 1′ 52° ➙ 0.58779 58802 58826 58849 58873 0.58896 58920 58943 58967 58990 0.59014 59037 59061 59084 59108 0.59131 59154 59178 59201 59225 0.59248 59272 59295 59318 59342 0.59365 59389 59412 59436 59459 0.59482 59506 59529 59552 59576 0.59599 59622 59646 59669 59693 0.59716 59739 59763 59786 59809 0.59832 59856 59879 59902 59926 0.59949 59972 59995 60019 60042 0.60065 60089 60112 60135 60158 0.60182 tan 593 126°➙ 143° ➙ Diff 1′ ➙ csc ➙ Diff 1′ ➙ ➙ ′ 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 sin ➙ 36°➙ TABLE Natural Trigonometric Functions 1′ sec Diff 1′ cot Diff 1′ 1.27994 27917 27841 27764 27688 1.27611 27535 27458 27382 27306 1.27230 27153 27077 27001 26925 1.26849 26774 26698 26622 26546 1.26471 26395 26319 26244 26169 1.26093 26018 25943 25867 25792 1.25717 25642 25567 25492 25417 1.25343 25268 25193 25118 25044 1.24969 24895 24820 24746 24672 1.24597 24523 24449 24375 24301 1.24227 24153 24079 24005 23931 1.23858 23784 23710 23637 23563 1.23490 tan 77 77 77 77 77 77 77 77 77 77 77 77 77 76 76 76 76 76 76 76 76 76 76 76 76 76 76 76 76 76 76 74 74 74 74 74 74 74 74 74 74 74 74 74 74 74 74 74 74 74 73 73 73 73 73 73 73 73 73 73 Diff 1′ 1.26902 26931 26960 26988 27017 1.27046 27075 27104 27133 27162 1.27191 27221 27250 27279 27308 1.27337 27366 27396 27425 27454 1.27483 27513 27542 27572 27601 1.27630 27660 27689 27719 27748 1.27778 27807 27837 27867 27896 1.27926 27956 27985 28015 28045 1.28075 28105 28134 28164 28194 1.28224 28254 28284 28314 28344 1.28374 28404 28434 28464 28495 1.28525 28555 28585 28615 28646 1.28676 csc Diff 1′ 29 29 28 29 29 29 29 29 29 29 30 29 29 29 29 29 30 29 29 29 30 29 30 29 29 30 29 30 29 30 29 30 30 29 30 30 29 30 30 30 30 29 30 30 30 30 30 30 30 30 30 30 30 31 30 30 30 30 31 30 Diff 1′ cos 0.78801 78783 78765 78747 78729 0.78711 78694 78676 78658 78640 0.78622 78604 78586 78568 78550 0.78532 78514 78496 78478 78460 0.78442 78424 78405 78387 78369 0.78351 78333 78315 78297 78279 0.78261 78243 78225 78206 78188 0.78170 78152 78134 78116 78098 0.78079 78061 78043 78025 78007 0.77988 77970 77952 77934 77916 0.77897 77879 77861 77843 77824 0.77806 77788 77769 77751 77733 0.77715 sin Diff 1′ 18 18 18 18 18 17 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 19 18 18 18 18 18 18 18 18 18 18 19 18 18 18 18 18 18 19 18 18 18 18 19 18 18 18 18 19 18 18 18 19 18 18 19 18 18 18 ′ 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 Diff 1′ 51° 39°➙ ′ 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 sin Diff 1′ csc Diff 1′ 0.62932 62955 62977 63000 63022 0.63045 63068 63090 63113 63135 0.63158 63180 63203 63225 63248 0.63271 63293 63316 63338 63361 0.63383 63406 63428 63451 63473 0.63496 63518 63540 63563 63585 0.63608 63630 63653 63675 63698 0.63720 63742 63765 63787 63810 0.63832 63854 63877 63899 63922 0.63944 63966 63989 64011 64033 0.64056 64078 64100 64123 64145 0.64167 64190 64212 64234 64256 0.64279 23 22 23 22 23 23 22 23 22 23 22 23 22 23 23 22 23 22 23 22 23 22 23 22 23 22 22 23 22 23 22 23 22 23 22 22 23 22 23 22 22 23 22 23 22 22 23 22 22 23 22 22 23 22 22 23 22 22 22 23 1.58902 58845 58788 58731 58674 1.58617 58560 58503 58447 58390 1.58333 58277 58221 58164 58108 1.58051 57995 57939 57883 57827 1.57771 57715 57659 57603 57547 1.57491 57436 57380 57324 57269 1.57213 57158 57103 57047 56992 1.56937 56881 56826 56771 56716 1.56661 56606 56551 56497 56442 1.56387 56332 56278 56223 56169 1.56114 56060 56005 55951 55897 1.55843 55789 55734 55680 55626 1.55572 58 57 57 57 57 57 57 57 57 57 57 57 57 57 57 57 57 57 57 57 56 56 56 56 56 56 56 56 56 56 56 56 56 56 56 56 56 56 56 54 54 54 54 54 54 54 54 54 54 54 54 54 54 54 54 54 54 54 54 53 ➙ Diff 46 47 47 47 47 47 47 47 47 47 47 47 47 47 48 47 47 47 47 48 47 47 48 47 47 48 47 48 47 48 47 48 47 48 47 48 48 47 48 48 47 48 48 48 47 48 48 48 48 48 48 48 48 48 48 48 48 48 48 48 sec 129°➙ cos Diff 1′ sec Diff 1′ tan 0.80978 81027 81075 81123 81171 0.81220 81268 81316 81364 81413 0.81461 81510 81558 81606 81655 0.81703 81752 81800 81849 81898 0.81946 81995 82044 82092 82141 0.82190 82238 82287 82336 82385 0.82434 82483 82531 82580 82629 0.82678 82727 82776 82825 82874 0.82923 82972 83022 83071 83120 0.83169 83218 83268 83317 83366 0.83415 83465 83514 83564 83613 0.83662 83712 83761 83811 83860 0.83910 cot Diff 1′ 49 48 48 48 49 48 48 48 49 48 49 48 48 49 48 49 48 49 49 48 49 49 48 49 49 48 49 49 49 49 49 48 49 49 49 49 49 49 49 49 49 50 49 49 49 49 50 49 49 49 50 49 50 49 49 50 49 50 49 50 Diff 1′ cot 1.23490 23416 23343 23270 23196 1.23123 23050 22977 22904 22831 1.22758 22685 22612 22539 22467 1.22394 22321 22249 22176 22104 1.22031 21959 21886 21814 21742 1.21670 21598 21526 21454 21382 1.21310 21238 21166 21094 21023 1.20951 20879 20808 20736 20665 1.20593 20522 20451 20379 20308 1.20237 20166 20095 20024 19953 1.19882 19811 19740 19669 19599 1.19528 19457 19387 19316 19246 1.19175 tan Diff 1′ 73 73 73 73 73 73 73 73 73 72 72 72 72 72 72 72 72 72 72 72 72 72 72 72 72 72 72 72 71 71 71 71 71 71 71 71 71 71 71 71 71 71 71 71 71 71 71 71 70 70 70 70 70 70 70 70 70 70 70 70 Diff 1′ sec 1.28676 28706 28737 28767 28797 1.28828 28858 28889 28919 28950 1.28980 29011 29042 29072 29103 1.29133 29164 29195 29226 29256 1.29287 29318 29349 29380 29411 1.29442 29473 29504 29535 29566 1.29597 29628 29659 29690 29721 1.29752 29784 29815 29846 29877 1.29909 29940 29971 30003 30034 1.30066 30097 30129 30160 30192 1.30223 30255 30287 30318 30350 1.30382 30413 30445 30477 30509 1.30541 csc Diff 1′ 30 31 30 30 31 30 31 30 31 30 31 31 30 31 30 31 31 31 30 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 32 31 31 31 32 31 31 32 31 32 31 32 31 32 31 32 32 31 32 32 31 32 32 32 32 Diff 1′ cos 140° 0.77715 77696 77678 77660 77641 0.77623 77605 77586 77568 77550 0.77531 77513 77494 77476 77458 0.77439 77421 77402 77384 77366 0.77347 77329 77310 77292 77273 0.77255 77236 77218 77199 77181 0.77162 77144 77125 77107 77088 0.77070 77051 77033 77014 76996 0.76977 76959 76940 76921 76903 0.76884 76866 76847 76828 76810 0.76791 76772 76754 76735 76717 0.76698 76679 76661 76642 76623 0.76604 sin Diff 1′ 19 18 18 19 18 18 19 18 18 19 18 19 18 18 19 18 19 18 18 19 18 19 18 19 18 19 18 19 18 19 18 19 18 19 18 19 18 19 18 19 18 19 19 18 19 18 19 19 18 19 19 18 19 18 19 19 18 19 19 19 ′ 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 Diff ➙ cos 0.78129 78175 78222 78269 78316 0.78363 78410 78457 78504 78551 0.78598 78645 78692 78739 78786 0.78834 78881 78928 78975 79022 0.79070 79117 79164 79212 79259 0.79306 79354 79401 79449 79496 0.79544 79591 79639 79686 79734 0.79781 79829 79877 79924 79972 0.80020 80067 80115 80163 80211 0.80258 80306 80354 80402 80450 0.80498 80546 80594 80642 80690 0.80738 80786 80834 80882 80930 0.80978 Diff 1′ ➙ 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 59 59 59 59 59 59 59 59 59 59 59 59 59 59 59 59 59 58 58 58 58 58 58 58 58 58 58 58 58 58 58 58 58 58 ➙ 1.62427 62366 62306 62246 62185 1.62125 62065 62005 61945 61885 1.61825 61765 61705 61646 61586 1.61526 61467 61407 61348 61288 1.61229 61170 61111 61051 60992 1.60933 60874 60815 60756 60698 1.60639 60580 60521 60463 60404 1.60346 60287 60229 60171 60112 1.60054 59996 59938 59880 59822 1.59764 59706 59648 59590 59533 1.59475 59418 59360 59302 59245 1.59188 59130 59073 59016 58959 1.58902 cot ➙ 23 23 23 23 23 23 22 23 23 23 23 23 23 23 22 23 23 23 23 23 22 23 23 23 23 22 23 23 23 22 23 23 23 22 23 23 23 22 23 23 23 22 23 23 22 23 23 22 23 23 22 23 23 22 23 23 22 23 22 23 Diff 1′ 1′ 50° ➙ 128°➙ 141° ➙ 0.61566 61589 61612 61635 61658 0.61681 61704 61726 61749 61772 0.61795 61818 61841 61864 61887 0.61909 61932 61955 61978 62001 0.62024 62046 62069 62092 62115 0.62138 62160 62183 62206 62229 0.62251 62274 62297 62320 62342 0.62365 62388 62411 62433 62456 0.62479 62502 62524 62547 62570 0.62592 62615 62638 62660 62683 0.62706 62728 62751 62774 62796 0.62819 62842 62864 62887 62909 0.62932 tan ➙ Diff 1′ ➙ csc ➙ ➙ ′ 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 Diff 1′ ➙ 38°➙ sin 594 TABLE Natural Trigonometric Functions TABLE TABLE Natural Trigonometric Functions Natural Trigonometric Functions 1′ sec Diff 1′ cot Diff 1′ 1.60033 59930 59826 59723 59620 1.59517 59414 59311 59208 59105 1.59002 58900 58797 58695 58593 1.58490 58388 58286 58184 58083 1.57981 57879 57778 57676 57575 1.57474 57372 57271 57170 57069 1.56969 56868 56767 56667 56566 1.56466 56366 56265 56165 56065 1.55966 55866 55766 55666 55567 1.55467 55368 55269 55170 55071 1.54972 54873 54774 54675 54576 1.54478 54379 54281 54183 54085 1.53986 tan 103 103 103 103 103 103 102 102 102 102 102 102 102 102 102 102 102 101 101 101 101 101 101 101 101 101 101 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 99 99 99 99 99 99 99 99 99 99 99 Diff 1′ 1.17918 17939 17961 17982 18004 1.18025 18047 18068 18090 18111 1.18133 18155 18176 18198 18220 1.18241 18263 18285 18307 18328 1.18350 18372 18394 18416 18437 1.18459 18481 18503 18525 18547 1.18569 18591 18613 18635 18657 1.18679 18701 18723 18745 18767 1.18790 18812 18834 18856 18878 1.18901 18923 18945 18967 18990 1.19012 19034 19057 19079 19102 1.19124 19146 19169 19191 19214 1.19236 csc Diff 1′ 21 22 21 22 21 22 21 22 21 22 22 21 22 22 21 22 22 22 21 22 22 22 22 21 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 23 22 22 22 22 23 22 22 22 23 22 22 23 22 23 22 22 23 22 23 22 Diff 1′ cos 0.84805 84789 84774 84759 84743 0.84728 84712 84697 84681 84666 0.84650 84635 84619 84604 84588 0.84573 84557 84542 84526 84511 0.84495 84480 84464 84448 84433 0.84417 84402 84386 84370 84355 0.84339 84324 84308 84292 84277 0.84261 84245 84230 84214 84198 0.84182 84167 84151 84135 84120 0.84104 84088 84072 84057 84041 0.84025 84009 83994 83978 83962 0.83946 83930 83915 83899 83883 0.83867 sin Diff 1′ 16 15 15 16 15 16 15 16 15 16 15 16 15 16 15 16 15 16 15 16 15 16 16 15 16 15 16 16 15 16 15 16 16 15 16 16 15 16 16 16 15 16 16 15 16 16 16 15 16 16 16 15 16 16 16 16 15 16 16 16 ′ 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 Diff 1′ 57° 33°➙ ′ 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 sin Diff 1′ csc Diff 1′ 0.54464 54488 54513 54537 54561 0.54586 54610 54635 54659 54683 0.54708 54732 54756 54781 54805 0.54829 54854 54878 54902 54927 0.54951 54975 54999 55024 55048 0.55072 55097 55121 55145 55169 0.55194 55218 55242 55266 55291 0.55315 55339 55363 55388 55412 0.55436 55460 55484 55509 55533 0.55557 55581 55605 55630 55654 0.55678 55702 55726 55750 55775 0.55799 55823 55847 55871 55895 0.55919 24 25 24 24 25 24 25 24 24 25 24 24 25 24 24 25 24 24 25 24 24 24 25 24 24 25 24 24 24 25 24 24 24 25 24 24 24 25 24 24 24 24 25 24 24 24 24 25 24 24 24 24 24 25 24 24 24 24 24 24 1.83608 83526 83444 83362 83280 1.83198 83116 83034 82953 82871 1.82790 82709 82627 82546 82465 1.82384 82303 82222 82142 82061 1.81981 81900 81820 81740 81659 1.81579 81499 81419 81340 81260 1.81180 81101 81021 80942 80862 1.80783 80704 80625 80546 80467 1.80388 80309 80231 80152 80074 1.79995 79917 79839 79761 79682 1.79604 79527 79449 79371 79293 1.79216 79138 79061 78984 78906 1.78829 82 82 82 81 81 81 81 81 81 81 81 81 81 81 80 80 80 80 80 80 80 80 80 80 80 80 80 80 80 80 80 80 80 80 80 80 80 79 79 79 79 79 79 79 79 79 79 79 79 78 78 78 78 78 78 78 78 78 78 78 ➙ Diff 40 41 40 41 40 41 40 41 41 40 41 40 41 41 40 41 41 40 41 41 41 40 41 41 41 41 40 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 42 41 41 41 41 42 41 41 41 42 41 41 42 sec 123°➙ cos Diff 1′ sec Diff 1′ tan 0.64941 64982 65024 65065 65106 0.65148 65189 65231 65272 65314 0.65355 65397 65438 65480 65521 0.65563 65604 65646 65688 65729 0.65771 65813 65854 65896 65938 0.65980 66021 66063 66105 66147 0.66189 66230 66272 66314 66356 0.66398 66440 66482 66524 66566 0.66608 66650 66692 66734 66776 0.66818 66860 66902 66944 66986 0.67028 67071 67113 67155 67197 0.67239 67282 67324 67366 67409 0.67451 cot Diff 1′ 41 42 41 41 42 41 42 41 42 41 42 41 42 41 42 41 42 42 41 42 42 41 42 42 42 41 42 42 42 42 41 42 42 42 42 42 42 42 42 42 42 42 42 42 42 42 42 42 42 42 43 42 42 42 42 43 42 42 43 42 Diff 1′ cot 1.53986 53888 53791 53693 53595 1.53497 53400 53302 53205 53107 1.53010 52913 52816 52719 52622 1.52525 52429 52332 52235 52139 1.52043 51946 51850 51754 51658 1.51562 51466 51370 51275 51179 1.51084 50988 50893 50797 50702 1.50607 50512 50417 50322 50228 1.50133 50038 49944 49849 49755 1.49661 49566 49472 49378 49284 1.49190 49097 49003 48909 48816 1.48722 48629 48536 48442 48349 1.48256 tan Diff 1′ 99 98 98 98 98 98 98 98 98 98 98 98 97 97 97 97 97 97 97 97 97 97 97 97 96 96 96 96 96 96 96 96 96 96 96 96 94 94 94 94 94 94 94 94 94 94 94 94 93 93 93 93 93 93 93 93 93 93 93 93 Diff 1′ sec 1.19236 19259 19281 19304 19327 1.19349 19372 19394 19417 19440 1.19463 19485 19508 19531 19553 1.19576 19599 19622 19645 19668 1.19691 19713 19736 19759 19782 1.19805 19828 19851 19874 19897 1.19920 19944 19967 19990 20013 1.20036 20059 20083 20106 20129 1.20152 20176 20199 20222 20246 1.20269 20292 20316 20339 20363 1.20386 20410 20433 20457 20480 1.20504 20527 20551 20575 20598 1.20622 csc Diff 1′ 23 22 23 23 22 23 22 23 23 23 22 23 23 22 23 23 23 23 23 23 22 23 23 23 23 23 23 23 23 23 24 23 23 23 23 23 24 23 23 23 24 23 23 24 23 23 24 23 24 23 24 23 24 23 24 23 24 24 23 24 Diff 1′ cos 146° 0.83867 83851 83835 83819 83804 0.83788 83772 83756 83740 83724 0.83708 83692 83676 83660 83645 0.83629 83613 83597 83581 83565 0.83549 83533 83517 83501 83485 0.83469 83453 83437 83421 83405 0.83389 83373 83356 83340 83324 0.83308 83292 83276 83260 83244 0.83228 83212 83195 83179 83163 0.83147 83131 83115 83098 83082 0.83066 83050 83034 83017 83001 0.82985 82969 82953 82936 82920 0.82904 sin Diff 1′ 16 16 16 15 16 16 16 16 16 16 16 16 16 15 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 17 16 16 16 16 16 16 16 16 16 17 16 16 16 16 16 17 16 16 16 16 17 16 16 16 16 17 16 16 ′ 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 Diff ➙ cos 0.62487 62527 62568 62608 62649 0.62689 62730 62770 62811 62852 0.62892 62933 62973 63014 63055 0.63095 63136 63177 63217 63258 0.63299 63340 63380 63421 63462 0.63503 63544 63584 63625 63666 0.63707 63748 63789 63830 63871 0.63912 63953 63994 64035 64076 0.64117 64158 64199 64240 64281 0.64322 64363 64404 64446 64487 0.64528 64569 64610 64652 64693 0.64734 64775 64817 64858 64899 0.64941 Diff 1′ ➙ 88 88 88 88 88 88 88 88 88 87 87 87 87 87 87 87 87 87 87 86 86 86 86 86 86 86 86 86 86 86 84 84 84 84 84 84 84 84 84 84 84 83 83 83 83 83 83 83 83 83 83 83 82 82 82 82 82 82 82 82 ➙ 1.88708 88620 88532 88445 88357 1.88270 88183 88095 88008 87921 1.87834 87748 87661 87574 87488 1.87401 87315 87229 87142 87056 1.86970 86885 86799 86713 86627 1.86542 86457 86371 86286 86201 1.86116 86031 85946 85861 85777 1.85692 85608 85523 85439 85355 1.85271 85187 85103 85019 84935 1.84852 84768 84685 84601 84518 1.84435 84352 84269 84186 84103 1.84020 83938 83855 83773 83690 1.83608 cot ➙ 25 24 25 25 24 25 24 25 25 24 25 25 24 25 24 25 25 24 25 24 25 25 24 25 24 25 24 25 24 25 24 25 25 24 25 24 25 24 25 24 25 24 25 24 24 25 24 25 24 25 24 25 24 24 25 24 25 24 25 24 Diff 1′ 1′ 56° ➙ 0.52992 53017 53041 53066 53091 0.53115 53140 53164 53189 53214 0.53238 53263 53288 53312 53337 0.53361 53386 53411 53435 53460 0.53484 53509 53534 53558 53583 0.53607 53632 53656 53681 53705 0.53730 53754 53779 53804 53828 0.53853 53877 53902 53926 53951 0.53975 54000 54024 54049 54073 0.54097 54122 54146 54171 54195 0.54220 54244 54269 54293 54317 0.54342 54366 54391 54415 54440 0.54464 tan 591 122°➙ 147° ➙ Diff 1′ ➙ csc ➙ Diff 1′ ➙ ➙ ′ 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 sin ➙ 32°➙ TABLE Natural Trigonometric Functions 1′ sec Diff 1′ cot Diff 1′ 1.48256 48163 48070 47977 47885 1.47792 47699 47607 47514 47422 1.47330 47238 47146 47053 46962 1.46870 46778 46686 46595 46503 1.46411 46320 46229 46137 46046 1.45955 45864 45773 45682 45592 1.45501 45410 45320 45229 45139 1.45049 44958 44868 44778 44688 1.44598 44508 44418 44329 44239 1.44149 44060 43970 43881 43792 1.43703 43614 43525 43436 43347 1.43258 43169 43080 42992 42903 1.42815 tan 92 92 92 92 92 92 92 92 92 92 92 92 92 91 91 91 91 91 91 91 91 91 91 91 91 91 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 89 89 89 89 89 89 89 89 Diff 1′ 1.20622 20645 20669 20693 20717 1.20740 20764 20788 20812 20836 1.20859 20883 20907 20931 20955 1.20979 21003 21027 21051 21075 1.21099 21123 21147 21171 21195 1.21220 21244 21268 21292 21316 1.21341 21365 21389 21414 21438 1.21462 21487 21511 21535 21560 1.21584 21609 21633 21658 21682 1.21707 21731 21756 21781 21805 1.21830 21855 21879 21904 21929 1.21953 21978 22003 22028 22053 1.22077 csc Diff 1′ 23 24 24 24 23 24 24 24 24 23 24 24 24 24 24 24 24 24 24 24 24 24 24 24 25 24 24 24 24 25 24 24 25 24 24 25 24 24 25 24 25 24 25 24 25 24 25 25 24 25 25 24 25 25 24 25 25 25 25 24 Diff 1′ cos 0.82904 82887 82871 82855 82839 0.82822 82806 82790 82773 82757 0.82741 82724 82708 82692 82675 0.82659 82643 82626 82610 82593 0.82577 82561 82544 82528 82511 0.82495 82478 82462 82446 82429 0.82413 82396 82380 82363 82347 0.82330 82314 82297 82281 82264 0.82248 82231 82214 82198 82181 0.82165 82148 82132 82115 82098 0.82082 82065 82048 82032 82015 0.81999 81982 81965 81949 81932 0.81915 sin Diff 1′ 17 16 16 16 17 16 16 17 16 16 17 16 16 17 16 16 17 16 17 16 16 17 16 17 16 17 16 16 17 16 17 16 17 16 17 16 17 16 17 16 17 17 16 17 16 17 16 17 17 16 17 17 16 17 16 17 17 16 17 17 ′ 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 Diff 1′ 55° 35°➙ ′ 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 sin Diff 1′ csc Diff 1′ 0.57358 57381 57405 57429 57453 0.57477 57501 57524 57548 57572 0.57596 57619 57643 57667 57691 0.57715 57738 57762 57786 57810 0.57833 57857 57881 57904 57928 0.57952 57976 57999 58023 58047 0.58070 58094 58118 58141 58165 0.58189 58212 58236 58260 58283 0.58307 58330 58354 58378 58401 0.58425 58449 58472 58496 58519 0.58543 58567 58590 58614 58637 0.58661 58684 58708 58731 58755 0.58779 23 24 24 24 24 24 23 24 24 24 23 24 24 24 24 23 24 24 24 23 24 24 23 24 24 24 23 24 24 23 24 24 23 24 24 23 24 24 23 24 23 24 24 23 24 24 23 24 23 24 24 23 24 23 24 23 24 23 24 24 1.74345 74272 74200 74128 74056 1.73983 73911 73840 73768 73696 1.73624 73552 73481 73409 73338 1.73267 73195 73124 73053 72982 1.72911 72840 72769 72698 72628 1.72557 72487 72416 72346 72275 1.72205 72135 72065 71995 71925 1.71855 71785 71715 71646 71576 1.71506 71437 71368 71298 71229 1.71160 71091 71022 70953 70884 1.70815 70746 70677 70609 70540 1.70472 70403 70335 70267 70198 1.70130 72 72 72 72 72 72 71 71 71 71 71 71 71 71 71 71 71 71 71 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 69 69 69 69 69 69 69 69 69 69 69 69 69 ➙ Diff 42 43 42 42 43 42 43 42 42 43 42 43 42 43 43 42 43 42 43 43 42 43 43 42 43 43 43 42 43 43 43 43 43 43 42 43 43 43 43 43 43 43 43 43 43 44 43 43 43 43 43 44 43 43 43 43 44 43 43 44 sec 125°➙ cos Diff 1′ sec Diff 1′ tan 0.70021 70064 70107 70151 70194 0.70238 70281 70325 70368 70412 0.70455 70499 70542 70586 70629 0.70673 70717 70760 70804 70848 0.70891 70935 70979 71023 71066 0.71110 71154 71198 71242 71285 0.71329 71373 71417 71461 71505 0.71549 71593 71637 71681 71725 0.71769 71813 71857 71901 71946 0.71990 72034 72078 72122 72167 0.72211 72255 72299 72344 72388 0.72432 72477 72521 72565 72610 0.72654 cot Diff 1′ 43 43 44 43 44 43 44 43 44 43 44 43 44 43 44 44 43 44 44 43 44 44 44 43 44 44 44 44 43 44 44 44 44 44 44 44 44 44 44 44 44 44 44 45 44 44 44 44 45 44 44 44 45 44 44 45 44 44 45 44 Diff 1′ cot 1.42815 42726 42638 42550 42462 1.42374 42286 42198 42110 42022 1.41934 41847 41759 41672 41584 1.41497 41409 41322 41235 41148 1.41061 40974 40887 40800 40714 1.40627 40540 40454 40367 40281 1.40195 40109 40022 39936 39850 1.39764 39679 39593 39507 39421 1.39336 39250 39165 39079 38994 1.38909 38824 38738 38653 38568 1.38484 38399 38314 38229 38145 1.38060 37976 37891 37807 37722 1.37638 tan Diff 1′ 89 89 89 89 89 89 88 88 88 88 88 88 88 88 88 88 88 88 88 88 87 87 87 87 87 87 87 87 87 87 87 87 87 87 86 86 86 86 86 86 86 86 86 86 86 86 86 86 84 84 84 84 84 84 84 84 84 84 84 84 Diff 1′ sec 1.22077 22102 22127 22152 22177 1.22202 22227 22252 22277 22302 1.22327 22352 22377 22402 22428 1.22453 22478 22503 22528 22554 1.22579 22604 22629 22655 22680 1.22706 22731 22756 22782 22807 1.22833 22858 22884 22909 22935 1.22960 22986 23012 23037 23063 1.23089 23114 23140 23166 23192 1.23217 23243 23269 23295 23321 1.23347 23373 23398 23424 23450 1.23476 23502 23529 23555 23581 1.23607 csc Diff 1′ 25 25 25 25 25 25 25 25 25 25 25 25 25 26 25 25 25 25 26 25 25 25 26 25 26 25 25 26 25 26 25 26 25 26 25 26 26 25 26 26 25 26 26 26 25 26 26 26 26 26 26 25 26 26 26 26 27 26 26 26 Diff 1′ cos 144° 0.81915 81899 81882 81865 81848 0.81832 81815 81798 81782 81765 0.81748 81731 81714 81698 81681 0.81664 81647 81631 81614 81597 0.81580 81563 81546 81530 81513 0.81496 81479 81462 81445 81428 0.81412 81395 81378 81361 81344 0.81327 81310 81293 81276 81259 0.81242 81225 81208 81191 81174 0.81157 81140 81123 81106 81089 0.81072 81055 81038 81021 81004 0.80987 80970 80953 80936 80919 0.80902 sin Diff 1′ 16 17 17 17 16 17 17 16 17 17 17 17 16 17 17 17 16 17 17 17 17 17 16 17 17 17 17 17 17 16 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 ′ 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 Diff ➙ cos 0.67451 67493 67536 67578 67620 0.67663 67705 67748 67790 67832 0.67875 67917 67960 68002 68045 0.68088 68130 68173 68215 68258 0.68301 68343 68386 68429 68471 0.68514 68557 68600 68642 68685 0.68728 68771 68814 68857 68900 0.68942 68985 69028 69071 69114 0.69157 69200 69243 69286 69329 0.69372 69416 69459 69502 69545 0.69588 69631 69675 69718 69761 0.69804 69847 69891 69934 69977 0.70021 Diff 1′ ➙ 78 77 77 77 77 77 77 77 77 77 77 77 77 77 76 76 76 76 76 76 76 76 76 76 76 76 74 74 74 74 74 74 74 74 74 74 74 74 74 73 73 73 73 73 73 73 73 73 73 73 73 73 72 72 72 72 72 72 72 72 ➙ 1.78829 78752 78675 78598 78521 1.78445 78368 78291 78215 78138 1.78062 77986 77910 77833 77757 1.77681 77606 77530 77454 77378 1.77303 77227 77152 77077 77001 1.76926 76851 76776 76701 76626 1.76552 76477 76402 76328 76253 1.76179 76105 76031 75956 75882 1.75808 75734 75661 75587 75513 1.75440 75366 75293 75219 75146 1.75073 75000 74927 74854 74781 1.74708 74635 74562 74490 74417 1.74345 cot ➙ 24 25 24 24 24 24 24 24 24 24 24 24 24 24 24 25 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 23 24 24 24 24 24 24 24 24 24 24 24 24 23 24 24 24 24 24 24 24 23 24 24 24 24 24 Diff 1′ 1′ 54° ➙ 124°➙ 145° ➙ 0.55919 55943 55968 55992 56016 0.56040 56064 56088 56112 56136 0.56160 56184 56208 56232 56256 0.56280 56305 56329 56353 56377 0.56401 56425 56449 56473 56497 0.56521 56545 56569 56593 56617 0.56641 56665 56689 56713 56736 0.56760 56784 56808 56832 56856 0.56880 56904 56928 56952 56976 0.57000 57024 57047 57071 57095 0.57119 57143 57167 57191 57215 0.57238 57262 57286 57310 57334 0.57358 tan ➙ Diff 1′ ➙ csc ➙ ➙ ′ 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 Diff 1′ ➙ 34°➙ sin 592 TABLE Natural Trigonometric Functions TABLE TABLE Natural Trigonometric Functions Natural Trigonometric Functions 1′ sec Diff 1′ cot Diff 1′ 1.88073 87941 87809 87677 87546 1.87415 87283 87152 87021 86891 1.86760 86630 86499 86369 86239 1.86109 85979 85850 85720 85591 1.85462 85333 85204 85075 84946 1.84818 84689 84561 84433 84305 1.84177 84049 83922 83794 83667 1.83540 83413 83286 83159 83033 1.82906 82780 82654 82528 82402 1.82276 82150 82025 81899 81774 1.81649 81524 81399 81274 81150 1.81025 80901 80777 80653 80529 1.80405 tan 131 131 131 131 131 131 131 130 130 130 130 130 130 130 130 130 130 130 130 130 130 129 129 129 129 129 129 129 128 128 128 128 128 128 128 128 127 127 127 127 127 127 127 126 126 126 126 126 126 126 126 124 124 124 124 124 124 124 123 123 Diff 1′ 1.13257 13275 13292 13310 13327 1.13345 13362 13380 13398 13415 1.13433 13451 13468 13486 13504 1.13521 13539 13557 13575 13593 1.13610 13628 13646 13664 13682 1.13700 13718 13735 13753 13771 1.13789 13807 13825 13843 13861 1.13879 13897 13915 13934 13952 1.13970 13988 14006 14024 14042 1.14061 14079 14097 14115 14134 1.14152 14170 14188 14207 14225 1.14243 14262 14280 14299 14317 1.14335 csc Diff 1′ 18 17 18 17 18 17 18 18 17 18 18 17 18 18 17 18 18 18 18 17 18 18 18 18 18 18 17 18 18 18 18 18 18 18 18 18 18 19 18 18 18 18 18 18 19 18 18 18 19 18 18 18 19 18 18 19 18 19 18 18 Diff 1′ cos 0.88295 88281 88267 88254 88240 0.88226 88213 88199 88185 88172 0.88158 88144 88130 88117 88103 0.88089 88075 88062 88048 88034 0.88020 88006 87993 87979 87965 0.87951 87937 87923 87909 87896 0.87882 87868 87854 87840 87826 0.87812 87798 87784 87770 87756 0.87743 87729 87715 87701 87687 0.87673 87659 87645 87631 87617 0.87603 87589 87575 87561 87546 0.87532 87518 87504 87490 87476 0.87462 sin Diff 1′ 14 14 13 14 14 13 14 14 13 14 14 14 13 14 14 14 13 14 14 14 14 13 14 14 14 14 14 14 13 14 14 14 14 14 14 14 14 14 14 13 14 14 14 14 14 14 14 14 14 14 14 14 14 15 14 14 14 14 14 14 ′ 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 Diff 1′ 61° 29°➙ ′ 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 sin Diff 1′ csc Diff 1′ 0.48481 48506 48532 48557 48583 0.48608 48634 48659 48684 48710 0.48735 48761 48786 48811 48837 0.48862 48888 48913 48938 48964 0.48989 49014 49040 49065 49090 0.49116 49141 49166 49192 49217 0.49242 49268 49293 49318 49344 0.49369 49394 49419 49445 49470 0.49495 49521 49546 49571 49596 0.49622 49647 49672 49697 49723 0.49748 49773 49798 49824 49849 0.49874 49899 49924 49950 49975 0.50000 25 26 25 26 25 26 25 25 26 25 26 25 25 26 25 26 25 25 26 25 25 26 25 25 26 25 25 26 25 25 26 25 25 26 25 25 25 26 25 25 26 25 25 25 26 25 25 25 26 25 25 25 26 25 25 25 25 26 25 25 2.06267 06158 06050 05942 05835 2.05727 05619 05512 05405 05298 2.05191 05084 04977 04870 04764 2.04657 04551 04445 04339 04233 2.04128 04022 03916 03811 03706 2.03601 03496 03391 03286 03182 2.03077 02973 02869 02765 02661 2.02557 02453 02349 02246 02143 2.02039 01936 01833 01730 01628 2.01525 01422 01320 01218 01116 2.01014 00912 00810 00708 00607 2.00505 00404 00303 00202 00101 2.00000 109 109 108 108 108 108 108 108 108 108 107 107 107 107 107 107 107 106 106 106 106 106 106 106 106 104 104 104 104 104 104 104 104 103 103 103 103 103 103 103 103 102 102 102 102 102 102 102 102 102 101 101 101 101 101 101 101 101 100 100 ➙ Diff 37 38 37 37 38 37 37 38 37 38 37 38 37 37 38 37 38 37 38 38 37 38 37 38 37 38 38 37 38 38 37 38 38 37 38 38 38 37 38 38 38 37 38 38 38 38 38 37 38 38 38 38 38 38 38 38 38 38 38 38 sec 119°➙ cos Diff 1′ sec Diff 1′ tan 0.55431 55469 55507 55545 55583 0.55621 55659 55697 55736 55774 0.55812 55850 55888 55926 55964 0.56003 56041 56079 56117 56156 0.56194 56232 56270 56309 56347 0.56385 56424 56462 56501 56539 0.56577 56616 56654 56693 56731 0.56769 56808 56846 56885 56923 0.56962 57000 57039 57078 57116 0.57155 57193 57232 57271 57309 0.57348 57386 57425 57464 57503 0.57541 57580 57619 57657 57696 0.57735 cot Diff 1′ 38 38 38 38 38 38 38 39 38 38 38 38 38 38 39 38 38 38 39 38 38 38 39 38 38 39 38 39 38 38 39 38 39 38 38 39 38 39 38 39 38 39 39 38 39 38 39 39 38 39 38 39 39 39 38 39 39 38 39 39 Diff 1′ cot 1.80405 80281 80158 80034 79911 1.79788 79665 79542 79419 79296 1.79174 79051 78929 78807 78685 1.78563 78441 78319 78198 78077 1.77955 77834 77713 77592 77471 1.77351 77230 77110 76990 76869 1.76749 76629 76510 76390 76271 1.76151 76032 75913 75794 75675 1.75556 75437 75319 75200 75082 1.74964 74846 74728 74610 74492 1.74375 74257 74140 74022 73905 1.73788 73671 73555 73438 73321 1.73205 tan Diff 1′ 123 123 123 123 123 123 122 122 122 122 122 122 122 122 121 121 121 121 121 121 121 121 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 120 119 119 119 119 119 119 119 119 118 118 118 118 118 118 118 118 118 117 117 117 117 117 Diff 1′ sec 1.14335 14354 14372 14391 14409 1.14428 14446 14465 14483 14502 1.14521 14539 14558 14576 14595 1.14614 14632 14651 14670 14689 1.14707 14726 14745 14764 14782 1.14801 14820 14839 14858 14877 1.14896 14914 14933 14952 14971 1.14990 15009 15028 15047 15066 1.15085 15105 15124 15143 15162 1.15181 15200 15219 15239 15258 1.15277 15296 15315 15335 15354 1.15373 15393 15412 15431 15451 1.15470 csc Diff 1′ 19 18 19 18 19 18 19 18 19 19 18 19 18 19 19 18 19 19 19 18 19 19 19 18 19 19 19 19 19 19 18 19 19 19 19 19 19 19 19 19 20 19 19 19 19 19 19 20 19 19 19 19 20 19 19 20 19 19 20 19 Diff 1′ cos 150° 0.87462 87448 87434 87420 87406 0.87391 87377 87363 87349 87335 0.87321 87306 87292 87278 87264 0.87250 87235 87221 87207 87193 0.87178 87164 87150 87136 87121 0.87107 87093 87079 87064 87050 0.87036 87021 87007 86993 86978 0.86964 86949 86935 86921 86906 0.86892 86878 86863 86849 86834 0.86820 86805 86791 86777 86762 0.86748 86733 86719 86704 86690 0.86675 86661 86646 86632 86617 0.86603 sin Diff 1′ 14 14 14 14 15 14 14 14 14 14 15 14 14 14 14 15 14 14 14 15 14 14 14 15 14 14 14 15 14 14 15 14 14 15 14 15 14 14 15 14 14 15 14 15 14 15 14 14 15 14 15 14 15 14 15 14 15 14 15 14 ′ 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 Diff ➙ cos 0.53171 53208 53246 53283 53320 0.53358 53395 53432 53470 53507 0.53545 53582 53620 53657 53694 0.53732 53769 53807 53844 53882 0.53920 53957 53995 54032 54070 0.54107 54145 54183 54220 54258 0.54296 54333 54371 54409 54446 0.54484 54522 54560 54597 54635 0.54673 54711 54748 54786 54824 0.54862 54900 54938 54975 55013 0.55051 55089 55127 55165 55203 0.55241 55279 55317 55355 55393 0.55431 Diff 1′ ➙ 117 117 117 117 116 116 116 116 116 116 116 114 114 114 114 114 114 114 113 113 113 113 113 113 113 112 112 112 112 112 112 112 111 111 111 111 111 111 111 110 110 110 110 110 110 110 110 110 110 110 110 110 110 110 109 109 109 109 109 109 ➙ 2.13005 12889 12773 12657 12540 2.12425 12309 12193 12078 11963 2.11847 11732 11617 11503 11388 2.11274 11159 11045 10931 10817 2.10704 10590 10477 10363 10250 2.10137 10024 09911 09799 09686 2.09574 09462 09350 09238 09126 2.09014 08903 08791 08680 08569 2.08458 08347 08236 08126 08015 2.07905 07795 07685 07575 07465 2.07356 07246 07137 07027 06918 2.06809 06701 06592 06483 06375 2.06267 cot ➙ 26 26 25 26 26 25 26 26 25 26 25 26 26 25 26 26 25 26 25 26 26 25 26 25 26 26 25 26 25 26 25 26 26 25 26 25 26 25 26 25 26 25 26 25 26 25 26 25 26 25 26 25 26 25 26 25 26 25 26 25 Diff 1′ 1′ 60° ➙ 0.46947 46973 46999 47024 47050 0.47076 47101 47127 47153 47178 0.47204 47229 47255 47281 47306 0.47332 47358 47383 47409 47434 0.47460 47486 47511 47537 47562 0.47588 47614 47639 47665 47690 0.47716 47741 47767 47793 47818 0.47844 47869 47895 47920 47946 0.47971 47997 48022 48048 48073 0.48099 48124 48150 48175 48201 0.48226 48252 48277 48303 48328 0.48354 48379 48405 48430 48456 0.48481 tan 589 118°➙ 151° ➙ Diff 1′ ➙ csc ➙ Diff 1′ ➙ ➙ ′ 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 sin ➙ 28°➙ TABLE Natural Trigonometric Functions 1′ sec Diff 1′ cot Diff 1′ 1.73205 73089 72973 72857 72741 1.72625 72509 72393 72278 72163 1.72047 71932 71817 71702 71588 1.71473 71358 71244 71129 71015 1.70901 70787 70673 70560 70446 1.70332 70219 70106 69992 69879 1.69766 69653 69541 69428 69316 1.69203 69091 68979 68866 68754 1.68643 68531 68419 68308 68196 1.68085 67974 67863 67752 67641 1.67530 67419 67309 67198 67088 1.66978 66867 66757 66647 66538 1.66428 tan 117 117 117 116 116 116 116 116 116 116 116 116 114 114 114 114 114 114 114 114 113 113 113 113 113 113 113 113 113 112 112 112 112 112 112 112 112 112 111 111 111 111 111 111 111 111 111 111 110 110 110 110 110 110 110 110 110 110 110 110 Diff 1′ 1.15470 15489 15509 15528 15548 1.15567 15587 15606 15626 15645 1.15665 15684 15704 15724 15743 1.15763 15782 15802 15822 15841 1.15861 15881 15901 15920 15940 1.15960 15980 16000 16019 16039 1.16059 16079 16099 16119 16139 1.16159 16179 16199 16219 16239 1.16259 16279 16299 16319 16339 1.16359 16380 16400 16420 16440 1.16460 16481 16501 16521 16541 1.16562 16582 16602 16623 16643 1.16663 csc Diff 1′ 19 20 19 20 19 20 19 20 19 20 19 20 20 19 20 19 20 20 19 20 20 20 19 20 20 20 20 19 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 21 20 20 20 20 21 20 20 20 21 20 20 21 20 20 Diff 1′ cos 0.86603 86588 86573 86559 86544 0.86530 86515 86501 86486 86471 0.86457 86442 86427 86413 86398 0.86384 86369 86354 86340 86325 0.86310 86295 86281 86266 86251 0.86237 86222 86207 86192 86178 0.86163 86148 86133 86119 86104 0.86089 86074 86059 86045 86030 0.86015 86000 85985 85970 85956 0.85941 85926 85911 85896 85881 0.85866 85851 85836 85821 85806 0.85792 85777 85762 85747 85732 0.85717 sin Diff 1′ 15 15 14 15 14 15 14 15 15 14 15 15 14 15 14 15 15 14 15 15 15 14 15 15 14 15 15 15 14 15 15 15 14 15 15 15 15 14 15 15 15 15 15 14 15 15 15 15 15 15 15 15 15 15 14 15 15 15 15 15 ′ 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 Diff 1′ 59° 31°➙ ′ 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 sin Diff 1′ csc Diff 1′ 0.51504 51529 51554 51579 51604 0.51628 51653 51678 51703 51728 0.51753 51778 51803 51828 51852 0.51877 51902 51927 51952 51977 0.52002 52026 52051 52076 52101 0.52126 52151 52175 52200 52225 0.52250 52275 52299 52324 52349 0.52374 52399 52423 52448 52473 0.52498 52522 52547 52572 52597 0.52621 52646 52671 52696 52720 0.52745 52770 52794 52819 52844 0.52869 52893 52918 52943 52967 0.52992 25 25 25 25 24 25 25 25 25 25 25 25 25 24 25 25 25 25 25 25 24 25 25 25 25 25 24 25 25 25 25 24 25 25 25 25 24 25 25 25 24 25 25 25 24 25 25 25 24 25 25 24 25 25 25 24 25 25 24 25 1.94160 94066 93973 93879 93785 1.93692 93598 93505 93412 93319 1.93226 93133 93040 92947 92855 1.92762 92670 92578 92486 92394 1.92302 92210 92118 92027 91935 1.91844 91752 91661 91570 91479 1.91388 91297 91207 91116 91026 1.90935 90845 90755 90665 90575 1.90485 90395 90305 90216 90126 1.90037 89948 89858 89769 89680 1.89591 89503 89414 89325 89237 1.89148 89060 88972 88884 88796 1.88708 93 93 93 93 93 93 93 93 93 92 92 92 92 92 92 92 92 92 92 91 91 91 91 91 91 91 91 91 91 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 89 89 89 89 89 89 89 89 89 89 88 88 ➙ Diff 39 39 38 39 39 39 39 39 39 39 38 39 39 39 39 39 39 39 39 39 39 39 40 39 39 39 39 39 39 40 39 39 39 39 40 39 39 39 40 39 39 40 39 39 40 39 40 39 39 40 39 40 39 40 39 40 39 40 39 40 sec 121°➙ cos Diff 1′ sec Diff 1′ tan 0.60086 60126 60165 60205 60245 0.60284 60324 60364 60403 60443 0.60483 60522 60562 60602 60642 0.60681 60721 60761 60801 60841 0.60881 60921 60960 61000 61040 0.61080 61120 61160 61200 61240 0.61280 61320 61360 61400 61440 0.61480 61520 61561 61601 61641 0.61681 61721 61761 61801 61842 0.61882 61922 61962 62003 62043 0.62083 62124 62164 62204 62245 0.62285 62325 62366 62406 62446 0.62487 cot Diff 1′ 40 39 40 40 39 40 40 39 40 40 39 40 40 40 39 40 40 40 40 40 40 39 40 40 40 40 40 40 40 40 40 40 40 40 40 40 41 40 40 40 40 40 40 41 40 40 40 41 40 40 41 40 40 41 40 40 41 40 40 41 Diff 1′ cot 1.66428 66318 66209 66099 65990 1.65881 65772 65663 65554 65445 1.65337 65228 65120 65011 64903 1.64795 64687 64579 64471 64363 1.64256 64148 64041 63934 63826 1.63719 63612 63505 63398 63292 1.63185 63079 62972 62866 62760 1.62654 62548 62442 62336 62230 1.62125 62019 61914 61808 61703 1.61598 61493 61388 61283 61179 1.61074 60970 60865 60761 60657 1.60553 60449 60345 60241 60137 1.60033 tan Diff 1′ 110 110 110 110 110 110 109 109 109 109 109 109 109 109 109 109 108 108 108 108 108 108 108 108 108 108 107 107 107 107 107 107 107 107 107 106 106 106 106 106 106 106 106 106 106 106 104 104 104 104 104 104 104 104 104 104 103 103 103 103 Diff 1′ sec 1.16663 16684 16704 16725 16745 1.16766 16786 16806 16827 16848 1.16868 16889 16909 16930 16950 1.16971 16992 17012 17033 17054 1.17075 17095 17116 17137 17158 1.17178 17199 17220 17241 17262 1.17283 17304 17325 17346 17367 1.17388 17409 17430 17451 17472 1.17493 17514 17535 17556 17577 1.17598 17620 17641 17662 17683 1.17704 17726 17747 17768 17790 1.17811 17832 17854 17875 17896 1.17918 csc Diff 1′ 21 20 21 20 21 20 20 21 21 20 21 20 21 20 21 21 20 21 21 21 20 21 21 21 20 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 21 22 21 21 21 21 22 21 21 22 21 21 22 21 21 22 Diff 1′ cos 148° 0.85717 85702 85687 85672 85657 0.85642 85627 85612 85597 85582 0.85567 85551 85536 85521 85506 0.85491 85476 85461 85446 85431 0.85416 85401 85385 85370 85355 0.85340 85325 85310 85294 85279 0.85264 85249 85234 85218 85203 0.85188 85173 85157 85142 85127 0.85112 85096 85081 85066 85051 0.85035 85020 85005 84989 84974 0.84959 84943 84928 84913 84897 0.84882 84866 84851 84836 84820 0.84805 sin Diff 1′ 15 15 15 15 15 15 15 15 15 15 16 15 15 15 15 15 15 15 15 15 15 16 15 15 15 15 15 16 15 15 15 15 16 15 15 15 16 15 15 15 16 15 15 15 16 15 15 16 15 15 16 15 15 16 15 16 15 15 16 15 ′ 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 Diff ➙ cos 0.57735 57774 57813 57851 57890 0.57929 57968 58007 58046 58085 0.58124 58162 58201 58240 58279 0.58318 58357 58396 58435 58474 0.58513 58552 58591 58631 58670 0.58709 58748 58787 58826 58865 0.58905 58944 58983 59022 59061 0.59101 59140 59179 59218 59258 0.59297 59336 59376 59415 59454 0.59494 59533 59573 59612 59651 0.59691 59730 59770 59809 59849 0.59888 59928 59967 60007 60046 0.60086 Diff 1′ ➙ 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 99 99 99 99 99 99 99 99 99 98 98 98 98 98 98 98 98 98 97 97 97 97 97 97 97 97 97 96 96 96 96 96 96 96 96 96 94 94 94 94 94 94 94 94 94 ➙ 2.00000 1.99899 99799 99698 99598 1.99498 99398 99298 99198 99098 1.98998 98899 98799 98700 98601 1.98502 98403 98304 98205 98107 1.98008 97910 97811 97713 97615 1.97517 97420 97322 97224 97127 1.97029 96932 96835 96738 96641 1.96544 96448 96351 96255 96158 1.96062 95966 95870 95774 95678 1.95583 95487 95392 95296 95201 1.95106 95011 94916 94821 94726 1.94632 94537 94443 94349 94254 1.94160 cot ➙ 25 25 26 25 25 25 25 25 26 25 25 25 25 25 25 26 25 25 25 25 25 25 25 25 25 26 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 Diff 1′ 1′ 58° ➙ 120°➙ 149° ➙ 0.50000 50025 50050 50076 50101 0.50126 50151 50176 50201 50227 0.50252 50277 50302 50327 50352 0.50377 50403 50428 50453 50478 0.50503 50528 50553 50578 50603 0.50628 50654 50679 50704 50729 0.50754 50779 50804 50829 50854 0.50879 50904 50929 50954 50979 0.51004 51029 51054 51079 51104 0.51129 51154 51179 51204 51229 0.51254 51279 51304 51329 51354 0.51379 51404 51429 51454 51479 0.51504 tan ➙ Diff 1′ ➙ csc ➙ ➙ ′ 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 Diff 1′ ➙ 30°➙ sin 590 TABLE Natural Trigonometric Functions TABLE TABLE Natural Trigonometric Functions Natural Trigonometric Functions 1′ sec Diff 1′ cot Diff 1′ 2.24604 24428 24252 24077 23902 2.23727 23553 23378 23204 23030 2.22857 22683 22510 22337 22164 2.21992 21819 21647 21475 21304 2.21132 20961 20790 20619 20449 2.20278 20108 19938 19769 19599 2.19430 19261 19092 18923 18755 2.18587 18419 18251 18084 17916 2.17749 17582 17416 17249 17083 2.16917 16751 16585 16420 16255 2.16090 15925 15760 15596 15432 2.15268 15104 14940 14777 14614 2.14451 tan 176 176 176 176 174 174 174 174 173 173 173 173 172 172 172 172 172 171 171 171 171 171 170 170 170 170 170 170 170 170 170 169 169 169 169 168 168 168 168 168 167 167 167 167 167 166 166 166 166 166 164 164 164 164 163 163 163 163 163 162 Diff 1′ 1.09464 09478 09492 09506 09520 1.09535 09549 09563 09577 09592 1.09606 09620 09635 09649 09663 1.09678 09692 09707 09721 09735 1.09750 09764 09779 09793 09808 1.09822 09837 09851 09866 09880 1.09895 09909 09924 09939 09953 1.09968 09982 09997 10012 10026 1.10041 10056 10071 10085 10100 1.10115 10130 10144 10159 10174 1.10189 10204 10218 10233 10248 1.10263 10278 10293 10308 10323 1.10338 csc Diff 1′ 14 14 14 14 15 14 14 14 15 14 14 15 14 14 15 14 15 14 14 15 14 15 14 15 14 15 14 15 14 15 14 15 15 14 15 14 15 15 14 15 15 15 14 15 15 15 14 15 15 15 15 14 15 15 15 15 15 15 15 15 Diff 1′ cos 0.91355 91343 91331 91319 91307 0.91295 91283 91272 91260 91248 0.91236 91224 91212 91200 91188 0.91176 91164 91152 91140 91128 0.91116 91104 91092 91080 91068 0.91056 91044 91032 91020 91008 0.90996 90984 90972 90960 90948 0.90936 90924 90911 90899 90887 0.90875 90863 90851 90839 90826 0.90814 90802 90790 90778 90766 0.90753 90741 90729 90717 90704 0.90692 90680 90668 90655 90643 0.90631 sin Diff 1′ 12 12 12 12 12 12 11 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 13 12 12 12 12 12 12 13 12 12 12 12 12 13 12 12 12 13 12 12 12 13 12 12 ′ 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 Diff 1′ 65° 25°➙ ′ 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 sin Diff 1′ csc Diff 1′ 0.42262 42288 42315 42341 42367 0.42394 42420 42446 42473 42499 0.42525 42552 42578 42604 42631 0.42657 42683 42709 42736 42762 0.42788 42815 42841 42867 42894 0.42920 42946 42972 42999 43025 0.43051 43077 43104 43130 43156 0.43182 43209 43235 43261 43287 0.43313 43340 43366 43392 43418 0.43445 43471 43497 43523 43549 0.43575 43602 43628 43654 43680 0.43706 43733 43759 43785 43811 0.43837 26 27 26 26 27 26 26 27 26 26 27 26 26 27 26 26 26 27 26 26 27 26 26 27 26 26 26 27 26 26 26 27 26 26 26 27 26 26 26 26 27 26 26 26 27 26 26 26 26 26 27 26 26 26 26 27 26 26 26 26 2.36620 36473 36325 36178 36031 2.35885 35738 35592 35446 35300 2.35154 35009 34863 34718 34573 2.34429 34284 34140 33996 33852 2.33708 33565 33422 33278 33135 2.32993 32850 32708 32566 32424 2.32282 32140 31999 31858 31717 2.31576 31436 31295 31155 31015 2.30875 30735 30596 30457 30318 2.30179 30040 29901 29763 29625 2.29487 29349 29211 29074 28937 2.28800 28663 28526 28390 28253 2.28117 148 148 148 147 147 147 147 147 146 146 146 146 146 144 144 144 144 144 143 143 143 143 143 142 142 142 142 142 141 141 141 141 141 140 140 140 140 140 140 140 140 140 140 140 139 139 139 139 139 138 138 138 138 138 138 137 137 137 137 137 ➙ Diff 35 35 34 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 36 35 35 35 35 35 35 36 35 35 35 35 36 35 35 35 36 35 35 35 36 35 35 36 35 35 36 35 36 35 35 36 sec 115°➙ cos Diff 1′ sec Diff 1′ tan 0.46631 46666 46702 46737 46772 0.46808 46843 46879 46914 46950 0.46985 47021 47056 47092 47128 0.47163 47199 47234 47270 47305 0.47341 47377 47412 47448 47483 0.47519 47555 47590 47626 47662 0.47698 47733 47769 47805 47840 0.47876 47912 47948 47984 48019 0.48055 48091 48127 48163 48198 0.48234 48270 48306 48342 48378 0.48414 48450 48486 48521 48557 0.48593 48629 48665 48701 48737 0.48773 cot Diff 1′ 35 36 35 35 36 35 36 35 36 35 36 35 36 36 35 36 35 36 35 36 36 35 36 35 36 36 35 36 36 36 35 36 36 35 36 36 36 36 35 36 36 36 36 35 36 36 36 36 36 36 36 36 35 36 36 36 36 36 36 36 Diff 1′ cot 2.14451 14288 14125 13963 13801 2.13639 13477 13316 13154 12993 2.12832 12671 12511 12350 12190 2.12030 11871 11711 11552 11392 2.11233 11075 10916 10758 10600 2.10442 10284 10126 09969 09811 2.09654 09498 09341 09184 09028 2.08872 08716 08560 08405 08250 2.08094 07939 07785 07630 07476 2.07321 07167 07014 06860 06706 2.06553 06400 06247 06094 05942 2.05790 05637 05485 05333 05182 2.05030 tan Diff 1′ 162 162 162 162 161 161 161 161 161 160 160 160 160 160 160 160 160 160 160 159 159 159 159 159 159 158 158 158 158 158 157 157 157 157 157 156 156 156 156 156 154 154 154 154 154 154 153 153 153 153 153 152 152 152 152 152 152 151 151 151 Diff 1′ sec 1.10338 10353 10368 10383 10398 1.10413 10428 10443 10458 10473 1.10488 10503 10518 10533 10549 1.10564 10579 10594 10609 10625 1.10640 10655 10670 10686 10701 1.10716 10731 10747 10762 10777 1.10793 10808 10824 10839 10854 1.10870 10885 10901 10916 10932 1.10947 10963 10978 10994 11009 1.11025 11041 11056 11072 11087 1.11103 11119 11134 11150 11166 1.11181 11197 11213 11229 11244 1.11260 csc Diff 1′ 15 15 15 15 15 15 15 15 15 15 15 15 15 16 15 15 15 15 16 15 15 15 16 15 15 15 16 15 15 16 15 16 15 15 16 15 16 15 16 15 16 15 16 15 16 16 15 16 15 16 16 15 16 16 15 16 16 16 15 16 Diff 1′ cos 154° 0.90631 90618 90606 90594 90582 0.90569 90557 90545 90532 90520 0.90507 90495 90483 90470 90458 0.90446 90433 90421 90408 90396 0.90383 90371 90358 90346 90334 0.90321 90309 90296 90284 90271 0.90259 90246 90233 90221 90208 0.90196 90183 90171 90158 90146 0.90133 90120 90108 90095 90082 0.90070 90057 90045 90032 90019 0.90007 89994 89981 89968 89956 0.89943 89930 89918 89905 89892 0.89879 sin Diff 1′ 13 12 12 12 13 12 12 13 12 13 12 12 13 12 12 13 12 13 12 13 12 13 12 12 13 12 13 12 13 12 13 13 12 13 12 13 12 13 12 13 13 12 13 13 12 13 12 13 13 12 13 13 13 12 13 13 12 13 13 13 ′ 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 Diff ➙ cos 0.44523 44558 44593 44627 44662 0.44697 44732 44767 44802 44837 0.44872 44907 44942 44977 45012 0.45047 45082 45117 45152 45187 0.45222 45257 45292 45327 45362 0.45397 45432 45467 45502 45538 0.45573 45608 45643 45678 45713 0.45748 45784 45819 45854 45889 0.45924 45960 45995 46030 46065 0.46101 46136 46171 46206 46242 0.46277 46312 46348 46383 46418 0.46454 46489 46525 46560 46595 0.46631 Diff 1′ ➙ 160 160 160 160 160 160 160 159 159 159 159 159 158 158 158 158 157 157 157 157 157 156 156 156 156 154 154 154 154 154 153 153 153 153 152 152 152 152 152 151 151 151 151 151 150 150 150 150 150 150 150 150 150 149 149 149 149 149 148 148 ➙ 2.45859 45699 45539 45378 45219 2.45059 44900 44741 44582 44423 2.44264 44106 43948 43790 43633 2.43476 43318 43162 43005 42848 2.42692 42536 42380 42225 42070 2.41914 41760 41605 41450 41296 2.41142 40988 40835 40681 40528 2.40375 40222 40070 39918 39766 2.39614 39462 39311 39159 39008 2.38857 38707 38556 38406 38256 2.38107 37957 37808 37658 37509 2.37361 37212 37064 36916 36768 2.36620 cot ➙ 26 27 26 27 26 27 27 26 27 26 27 26 27 26 27 26 27 26 27 26 27 26 27 26 27 26 27 26 27 26 27 26 27 26 27 26 27 26 26 27 26 27 26 27 26 26 27 26 27 26 26 27 26 27 26 26 27 26 26 27 Diff 1′ 1′ 64° ➙ 0.40674 40700 40727 40753 40780 0.40806 40833 40860 40886 40913 0.40939 40966 40992 41019 41045 0.41072 41098 41125 41151 41178 0.41204 41231 41257 41284 41310 0.41337 41363 41390 41416 41443 0.41469 41496 41522 41549 41575 0.41602 41628 41655 41681 41707 0.41734 41760 41787 41813 41840 0.41866 41892 41919 41945 41972 0.41998 42024 42051 42077 42104 0.42130 42156 42183 42209 42235 0.42262 tan 587 114°➙ 155° ➙ Diff 1′ ➙ csc ➙ Diff 1′ ➙ ➙ ′ 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 sin ➙ 24°➙ TABLE Natural Trigonometric Functions 1′ sec Diff 1′ cot Diff 1′ 2.05030 04879 04728 04577 04426 2.04276 04125 03975 03825 03675 2.03526 03376 03227 03078 02929 2.02780 02631 02483 02335 02187 2.02039 01891 01743 01596 01449 2.01302 01155 01008 00862 00715 2.00569 00423 00277 2.00131 1.99986 1.99841 99695 99550 99406 99261 1.99116 98972 98828 98684 98540 1.98396 98253 98110 97966 97823 1.97681 97538 97395 97253 97111 1.96969 96827 96685 96544 96402 1.96261 tan 151 151 150 150 150 150 150 150 150 150 150 150 150 149 149 149 149 149 149 148 148 148 148 148 148 147 147 147 147 147 147 146 146 146 146 146 146 144 144 144 144 144 144 143 143 143 143 143 143 142 142 142 142 142 142 141 141 141 141 141 Diff 1′ 1.11260 11276 11292 11308 11323 1.11339 11355 11371 11387 11403 1.11419 11435 11451 11467 11483 1.11499 11515 11531 11547 11563 1.11579 11595 11611 11627 11643 1.11659 11675 11691 11708 11724 1.11740 11756 11772 11789 11805 1.11821 11838 11854 11870 11886 1.11903 11919 11936 11952 11968 1.11985 12001 12018 12034 12051 1.12067 12083 12100 12117 12133 1.12150 12166 12183 12199 12216 1.12233 csc Diff 1′ 16 16 16 15 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 17 16 16 16 16 17 16 16 17 16 16 16 17 16 17 16 16 17 16 17 16 17 16 16 17 17 16 17 16 17 16 17 17 Diff 1′ cos 0.89879 89867 89854 89841 89828 0.89816 89803 89790 89777 89764 0.89752 89739 89726 89713 89700 0.89687 89674 89662 89649 89636 0.89623 89610 89597 89584 89571 0.89558 89545 89532 89519 89506 0.89493 89480 89467 89454 89441 0.89428 89415 89402 89389 89376 0.89363 89350 89337 89324 89311 0.89298 89285 89272 89259 89245 0.89232 89219 89206 89193 89180 0.89167 89153 89140 89127 89114 0.89101 sin Diff 1′ 12 13 13 13 12 13 13 13 13 12 13 13 13 13 13 13 12 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 14 13 13 13 13 13 13 14 13 13 13 13 ′ 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 Diff 1′ 63° 27°➙ ′ 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 sin Diff 1′ csc Diff 1′ 0.45399 45425 45451 45477 45503 0.45529 45554 45580 45606 45632 0.45658 45684 45710 45736 45762 0.45787 45813 45839 45865 45891 0.45917 45942 45968 45994 46020 0.46046 46072 46097 46123 46149 0.46175 46201 46226 46252 46278 0.46304 46330 46355 46381 46407 0.46433 46458 46484 46510 46536 0.46561 46587 46613 46639 46664 0.46690 46716 46742 46767 46793 0.46819 46844 46870 46896 46921 0.46947 26 26 26 26 26 25 26 26 26 26 26 26 26 26 25 26 26 26 26 26 25 26 26 26 26 26 25 26 26 26 26 25 26 26 26 26 25 26 26 26 25 26 26 26 25 26 26 26 25 26 26 26 25 26 26 25 26 26 25 26 2.20269 20143 20018 19892 19767 2.19642 19517 19393 19268 19144 2.19019 18895 18772 18648 18524 2.18401 18277 18154 18031 17909 2.17786 17663 17541 17419 17297 2.17175 17053 16932 16810 16689 2.16568 16447 16326 16206 16085 2.15965 15845 15725 15605 15485 2.15366 15246 15127 15008 14889 2.14770 14651 14533 14414 14296 2.14178 14060 13942 13825 13707 2.13590 13473 13356 13239 13122 2.13005 126 126 126 126 126 124 124 124 124 124 124 123 123 123 123 123 123 122 122 122 122 122 122 122 121 121 121 121 121 121 120 120 120 120 120 120 120 120 120 120 120 120 120 119 119 119 119 119 119 119 118 118 118 118 118 118 118 117 117 117 ➙ Diff 36 36 36 36 36 36 37 36 36 36 36 36 36 36 37 36 36 36 36 36 37 36 36 36 37 36 36 37 36 36 36 37 36 37 36 36 37 36 36 37 36 37 36 37 36 37 36 37 36 37 36 37 36 37 36 37 37 36 37 37 sec 117°➙ cos Diff 1′ sec Diff 1′ tan 0.50953 50989 51026 51063 51099 0.51136 51173 51209 51246 51283 0.51319 51356 51393 51430 51467 0.51503 51540 51577 51614 51651 0.51688 51724 51761 51798 51835 0.51872 51909 51946 51983 52020 0.52057 52094 52131 52168 52205 0.52242 52279 52316 52353 52390 0.52427 52464 52501 52538 52575 0.52613 52650 52687 52724 52761 0.52798 52836 52873 52910 52947 0.52985 53022 53059 53096 53134 0.53171 cot Diff 1′ 36 37 37 36 37 37 36 37 37 36 37 37 37 37 36 37 37 37 37 37 36 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37 38 37 37 37 37 37 38 37 37 37 38 37 37 37 38 37 Diff 1′ cot 1.96261 96120 95979 95838 95698 1.95557 95417 95277 95137 94997 1.94858 94718 94579 94440 94301 1.94162 94023 93885 93746 93608 1.93470 93332 93195 93057 92920 1.92782 92645 92508 92371 92235 1.92098 91962 91826 91690 91554 1.91418 91282 91147 91012 90876 1.90741 90607 90472 90337 90203 1.90069 89935 89801 89667 89533 1.89400 89266 89133 89000 88867 1.88734 88602 88469 88337 88205 1.88073 tan Diff 1′ 141 140 140 140 140 140 140 140 140 140 140 140 140 139 139 139 139 139 139 139 138 138 138 138 138 138 137 137 137 137 137 137 137 136 136 136 136 136 136 134 134 134 134 134 134 134 133 133 133 133 133 133 133 132 132 132 132 132 132 132 Diff 1′ sec 1.12233 12249 12266 12283 12299 1.12316 12333 12349 12366 12383 1.12400 12416 12433 12450 12467 1.12484 12501 12518 12534 12551 1.12568 12585 12602 12619 12636 1.12653 12670 12687 12704 12721 1.12738 12755 12772 12789 12807 1.12824 12841 12858 12875 12892 1.12910 12927 12944 12961 12979 1.12996 13013 13031 13048 13065 1.13083 13100 13117 13135 13152 1.13170 13187 13205 13222 13239 1.13257 csc Diff 1′ 16 17 17 16 17 17 16 17 17 17 16 17 17 17 17 17 17 16 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 18 17 17 17 17 17 18 17 17 17 18 17 17 18 17 17 18 17 17 18 17 18 17 18 17 17 18 Diff 1′ cos 152° 0.89101 89087 89074 89061 89048 0.89035 89021 89008 88995 88981 0.88968 88955 88942 88928 88915 0.88902 88888 88875 88862 88848 0.88835 88822 88808 88795 88782 0.88768 88755 88741 88728 88715 0.88701 88688 88674 88661 88647 0.88634 88620 88607 88593 88580 0.88566 88553 88539 88526 88512 0.88499 88485 88472 88458 88445 0.88431 88417 88404 88390 88377 0.88363 88349 88336 88322 88308 0.88295 sin Diff 1′ 14 13 13 13 13 14 13 13 14 13 13 13 14 13 13 14 13 13 14 13 13 14 13 13 14 13 14 13 13 14 13 14 13 14 13 14 13 14 13 14 13 14 13 14 13 14 13 14 13 14 14 13 14 13 14 14 13 14 14 13 ′ 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 Diff ➙ cos 0.48773 48809 48845 48881 48917 0.48953 48989 49026 49062 49098 0.49134 49170 49206 49242 49278 0.49315 49351 49387 49423 49459 0.49495 49532 49568 49604 49640 0.49677 49713 49749 49786 49822 0.49858 49894 49931 49967 50004 0.50040 50076 50113 50149 50185 0.50222 50258 50295 50331 50368 0.50404 50441 50477 50514 50550 0.50587 50623 50660 50696 50733 0.50769 50806 50843 50879 50916 0.50953 Diff 1′ ➙ 136 136 136 136 136 136 134 134 134 134 134 133 133 133 133 133 133 132 132 132 132 132 132 131 131 131 131 131 131 130 130 130 130 130 130 130 130 130 130 130 129 129 129 129 129 129 128 128 128 128 128 128 127 127 127 127 127 127 126 126 ➙ 2.28117 27981 27845 27710 27574 2.27439 27304 27169 27035 26900 2.26766 26632 26498 26364 26230 2.26097 25963 25830 25697 25565 2.25432 25300 25167 25035 24903 2.24772 24640 24509 24378 24247 2.24116 23985 23855 23724 23594 2.23464 23334 23205 23075 22946 2.22817 22688 22559 22430 22302 2.22174 22045 21918 21790 21662 2.21535 21407 21280 21153 21026 2.20900 20773 20647 20521 20395 2.20269 cot ➙ 26 26 27 26 26 26 26 26 26 26 26 27 26 26 26 26 26 26 26 26 26 26 26 27 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 25 26 26 26 26 26 26 Diff 1′ 1′ 62° ➙ 116°➙ 153° ➙ 0.43837 43863 43889 43916 43942 0.43968 43994 44020 44046 44072 0.44098 44124 44151 44177 44203 0.44229 44255 44281 44307 44333 0.44359 44385 44411 44437 44464 0.44490 44516 44542 44568 44594 0.44620 44646 44672 44698 44724 0.44750 44776 44802 44828 44854 0.44880 44906 44932 44958 44984 0.45010 45036 45062 45088 45114 0.45140 45166 45192 45218 45243 0.45269 45295 45321 45347 45373 0.45399 tan ➙ Diff 1′ ➙ csc ➙ ➙ ′ 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 Diff 1′ ➙ 26°➙ sin 588 TABLE Natural Trigonometric Functions TABLE TABLE Natural Trigonometric Functions Natural Trigonometric Functions sec Diff 1′ cot Diff 1′ tan 249 249 248 248 247 247 247 246 246 244 244 244 243 243 243 242 242 241 241 241 240 240 240 240 240 239 239 239 238 238 237 237 237 236 236 236 234 234 234 233 233 232 232 232 231 231 231 230 230 230 230 230 230 229 229 229 228 228 228 227 Diff 1′ 1.06418 06429 06440 06452 06463 1.06474 06486 06497 06508 06520 1.06531 06542 06554 06565 06577 1.06588 06600 06611 06622 06634 1.06645 06657 06668 06680 06691 1.06703 06715 06726 06738 06749 1.06761 06773 06784 06796 06807 1.06819 06831 06842 06854 06866 1.06878 06889 06901 06913 06925 1.06936 06948 06960 06972 06984 1.06995 07007 07019 07031 07043 1.07055 07067 07079 07091 07103 1.07114 csc Diff 1′ 11 11 12 11 11 12 11 11 12 11 11 12 11 12 11 12 11 11 12 11 12 11 12 11 12 12 11 12 11 12 12 11 12 11 12 12 11 12 12 12 11 12 12 12 11 12 12 12 12 11 12 12 12 12 12 12 12 12 12 11 Diff 1′ cos 0.93969 93959 93949 93939 93929 0.93919 93909 93899 93889 93879 0.93869 93859 93849 93839 93829 0.93819 93809 93799 93789 93779 0.93769 93759 93748 93738 93728 0.93718 93708 93698 93688 93677 0.93667 93657 93647 93637 93626 0.93616 93606 93596 93585 93575 0.93565 93555 93544 93534 93524 0.93514 93503 93493 93483 93472 0.93462 93452 93441 93431 93420 0.93410 93400 93389 93379 93368 0.93358 sin Diff 1′ 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 11 10 10 10 10 10 10 11 10 10 10 10 11 10 10 10 11 10 10 10 11 10 10 10 11 10 10 11 10 10 11 10 11 10 10 11 10 11 10 ′ 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 Diff 1′ 69° 21°➙ ′ 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 sin Diff 1′ csc Diff 1′ 0.35837 35864 35891 35918 35945 0.35973 36000 36027 36054 36081 0.36108 36135 36162 36190 36217 0.36244 36271 36298 36325 36352 0.36379 36406 36434 36461 36488 0.36515 36542 36569 36596 36623 0.36650 36677 36704 36731 36758 0.36785 36812 36839 36867 36894 0.36921 36948 36975 37002 37029 0.37056 37083 37110 37137 37164 0.37191 37218 37245 37272 37299 0.37326 37353 37380 37407 37434 0.37461 27 27 27 27 28 27 27 27 27 27 27 27 28 27 27 27 27 27 27 27 27 28 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27 28 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27 2.79043 78832 78621 78410 78200 2.77990 77780 77571 77362 77154 2.76945 76737 76530 76323 76116 2.75909 75703 75497 75292 75086 2.74881 74677 74473 74269 74065 2.73862 73659 73456 73254 73052 2.72850 72649 72448 72247 72047 2.71847 71647 71448 71249 71050 2.70851 70653 70455 70258 70061 2.69864 69667 69471 69275 69079 2.68884 68689 68494 68299 68105 2.67911 67718 67525 67332 67139 2.66947 211 210 210 210 210 210 210 209 209 209 208 208 208 207 207 207 206 206 206 204 204 204 203 203 203 202 202 202 201 201 201 201 200 200 200 200 200 200 199 199 199 198 198 198 197 197 197 196 196 196 196 194 194 194 193 193 193 192 192 192 111°➙ cos Diff 1′ sec Diff 1′ tan 0.38386 38420 38453 38487 38520 0.38553 38587 38620 38654 38687 0.38721 38754 38787 38821 38854 0.38888 38921 38955 38988 39022 0.39055 39089 39122 39156 39190 0.39223 39257 39290 39324 39357 0.39391 39425 39458 39492 39526 0.39559 39593 39626 39660 39694 0.39727 39761 39795 39829 39862 0.39896 39930 39963 39997 40031 0.40065 40098 40132 40166 40200 0.40234 40267 40301 40335 40369 0.40403 cot Diff 1′ 34 33 34 33 33 34 33 34 33 34 33 33 34 33 34 33 34 33 34 33 34 33 34 34 33 34 33 34 33 34 34 33 34 34 33 34 33 34 34 33 34 34 34 33 34 34 33 34 34 34 33 34 34 34 34 33 34 34 34 34 Diff 1′ cot 2.60509 60283 60057 59831 59606 2.59381 59156 58932 58708 58484 2.58261 58038 57815 57593 57371 2.57150 56928 56707 56487 56266 2.56046 55827 55608 55389 55170 2.54952 54734 54516 54299 54082 2.53865 53648 53432 53217 53001 2.52786 52571 52357 52142 51929 2.51715 51502 51289 51076 50864 2.50652 50440 50229 50018 49807 2.49597 49386 49177 48967 48758 2.48549 48340 48132 47924 47716 2.47509 tan Diff 1′ 227 226 226 226 224 224 224 223 223 223 222 222 222 221 221 221 220 220 220 220 220 220 219 219 219 219 218 218 218 217 217 217 216 216 216 214 214 214 213 213 213 212 212 212 211 211 211 211 210 210 210 210 210 210 209 209 209 209 208 208 Diff 1′ sec 1.07114 07126 07138 07150 07162 1.07174 07186 07199 07211 07223 1.07235 07247 07259 07271 07283 1.07295 07307 07320 07332 07344 1.07356 07368 07380 07393 07405 1.07417 07429 07442 07454 07466 1.07479 07491 07503 07516 07528 1.07540 07553 07565 07578 07590 1.07602 07615 07627 07640 07652 1.07665 07677 07690 07702 07715 1.07727 07740 07752 07765 07778 1.07790 07803 07816 07828 07841 1.07853 csc Diff 1′ 12 12 12 12 12 12 13 12 12 12 12 12 12 12 12 12 13 12 12 12 12 12 13 12 12 12 13 12 12 13 12 12 13 12 12 13 12 13 12 12 13 12 13 12 13 12 13 12 13 12 13 12 13 13 12 13 13 12 13 12 Diff 1′ cos 158° 0.93358 93348 93337 93327 93316 0.93306 93295 93285 93274 93264 0.93253 93243 93232 93222 93211 0.93201 93190 93180 93169 93159 0.93148 93137 93127 93116 93106 0.93095 93084 93074 93063 93052 0.93042 93031 93020 93010 92999 0.92988 92978 92967 92956 92945 0.92935 92924 92913 92902 92892 0.92881 92870 92859 92849 92838 0.92827 92816 92805 92794 92784 0.92773 92762 92751 92740 92729 0.92718 sin Diff 1′ 10 11 10 11 10 11 10 11 10 11 10 11 10 11 10 11 10 11 10 11 11 10 11 10 11 11 10 11 11 10 11 11 10 11 11 10 11 11 11 10 11 11 11 10 11 11 11 10 11 11 11 11 11 10 11 11 11 11 11 11 ′ 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 Diff 1′ 68° 585 1′ 2.74748 74499 74251 74004 73756 2.73509 73263 73017 72771 72526 2.72281 72036 71792 71548 71305 2.71062 70819 70577 70335 70094 2.69853 69612 69371 69131 68892 2.68653 68414 68175 67937 67700 2.67462 67225 66989 66752 66516 2.66281 66046 65811 65576 65342 2.65109 64875 64642 64410 64177 2.63945 63714 63483 63252 63021 2.62791 62561 62332 62103 61874 2.61646 61418 61190 60963 60736 2.60509 sec ➙ Diff 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33 34 33 33 33 33 33 33 33 34 33 33 33 33 34 33 33 33 33 34 33 33 33 34 33 33 33 34 33 33 34 33 33 34 33 33 34 33 33 Diff 1′ ➙ cos 0.36397 36430 36463 36496 36529 0.36562 36595 36628 36661 36694 0.36727 36760 36793 36826 36859 0.36892 36925 36958 36991 37024 0.37057 37090 37123 37157 37190 0.37223 37256 37289 37322 37355 0.37388 37422 37455 37488 37521 0.37554 37588 37621 37654 37687 0.37720 37754 37787 37820 37853 0.37887 37920 37953 37986 38020 0.38053 38086 38120 38153 38186 0.38220 38253 38286 38320 38353 0.38386 cot ➙ 233 233 232 232 231 231 231 230 230 230 230 230 229 229 229 228 228 227 227 227 226 226 224 224 224 223 223 223 222 222 221 221 221 220 220 220 220 220 220 219 219 218 218 218 217 217 217 216 216 216 214 214 214 213 213 213 212 212 211 211 ➙ 2.92380 92147 91914 91681 91449 2.91217 90986 90754 90524 90293 2.90063 89834 89605 89376 89148 2.88920 88692 88465 88238 88011 2.87785 87560 87334 87109 86885 2.86661 86437 86213 85990 85767 2.85545 85323 85102 84880 84659 2.84439 84219 83999 83780 83561 2.83342 83124 82906 82688 82471 2.82254 82037 81821 81605 81390 2.81175 80960 80746 80531 80318 2.80104 79891 79679 79466 79254 2.79043 Diff 1′ ➙ 27 28 27 27 28 27 27 28 27 27 28 27 27 27 28 27 27 28 27 27 27 28 27 27 27 28 27 27 27 28 27 27 27 28 27 27 27 28 27 27 27 27 28 27 27 27 28 27 27 27 27 27 28 27 27 27 27 27 28 27 tan ➙ 0.34202 34229 34257 34284 34311 0.34339 34366 34393 34421 34448 0.34475 34503 34530 34557 34584 0.34612 34639 34666 34694 34721 0.34748 34775 34803 34830 34857 0.34884 34912 34939 34966 34993 0.35021 35048 35075 35102 35130 0.35157 35184 35211 35239 35266 0.35293 35320 35347 35375 35402 0.35429 35456 35484 35511 35538 0.35565 35592 35619 35647 35674 0.35701 35728 35755 35782 35810 0.35837 110°➙ 159° ➙ Diff 1′ ➙ csc ➙ Diff 1′ ➙ ➙ ′ 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 sin ➙ 20°➙ TABLE Natural Trigonometric Functions 1′ sec Diff 1′ cot Diff 1′ 2.47509 47302 47095 46888 46682 2.46476 46270 46065 45860 45655 2.45451 45246 45043 44839 44636 2.44433 44230 44027 43825 43623 2.43422 43220 43019 42819 42618 2.42418 42218 42019 41819 41620 2.41421 41223 41025 40827 40629 2.40432 40235 40038 39841 39645 2.39449 39253 39058 38863 38668 2.38473 38279 38084 37891 37697 2.37504 37311 37118 36925 36733 2.36541 36349 36158 35967 35776 2.35585 tan 208 207 207 207 206 206 206 206 204 204 204 203 203 203 203 202 202 202 201 201 201 201 200 200 200 200 200 200 200 199 199 199 198 198 198 198 197 197 197 197 196 196 196 194 194 194 194 193 193 193 193 192 192 192 191 191 191 191 190 190 Diff 1′ 1.07853 07866 07879 07892 07904 1.07917 07930 07943 07955 07968 1.07981 07994 08006 08019 08032 1.08045 08058 08071 08084 08097 1.08109 08122 08135 08148 08161 1.08174 08187 08200 08213 08226 1.08239 08252 08265 08278 08291 1.08305 08318 08331 08344 08357 1.08370 08383 08397 08410 08423 1.08436 08449 08463 08476 08489 1.08503 08516 08529 08542 08556 1.08569 08582 08596 08609 08623 1.08636 csc Diff 1′ 13 13 13 12 13 13 13 12 13 13 13 12 13 13 13 13 13 13 13 12 13 13 13 13 13 13 13 13 13 13 13 13 13 13 14 13 13 13 13 13 13 14 13 13 13 13 14 13 13 14 13 13 13 14 13 13 14 13 14 13 Diff 1′ cos 0.92718 92707 92697 92686 92675 0.92664 92653 92642 92631 92620 0.92609 92598 92587 92576 92565 0.92554 92543 92532 92521 92510 0.92499 92488 92477 92466 92455 0.92444 92432 92421 92410 92399 0.92388 92377 92366 92355 92343 0.92332 92321 92310 92299 92287 0.92276 92265 92254 92243 92231 0.92220 92209 92198 92186 92175 0.92164 92152 92141 92130 92119 0.92107 92096 92085 92073 92062 0.92050 sin Diff 1′ 11 10 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 12 11 11 11 11 11 11 11 12 11 11 11 11 12 11 11 11 11 12 11 11 11 12 11 11 12 11 11 11 12 11 11 12 11 12 ′ 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 Diff 1′ 67° 23°➙ ′ 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 sin Diff 1′ csc Diff 1′ 0.39073 39100 39127 39153 39180 0.39207 39234 39260 39287 39314 0.39341 39367 39394 39421 39448 0.39474 39501 39528 39555 39581 0.39608 39635 39661 39688 39715 0.39741 39768 39795 39822 39848 0.39875 39902 39928 39955 39982 0.40008 40035 40062 40088 40115 0.40141 40168 40195 40221 40248 0.40275 40301 40328 40355 40381 0.40408 40434 40461 40488 40514 0.40541 40567 40594 40621 40647 0.40674 27 27 26 27 27 27 26 27 27 27 26 27 27 27 26 27 27 27 26 27 27 26 27 27 26 27 27 27 26 27 27 26 27 27 26 27 27 26 27 26 27 27 26 27 27 26 27 27 26 27 26 27 27 26 27 26 27 27 26 27 2.55930 55755 55580 55405 55231 2.55057 54883 54709 54536 54363 2.54190 54017 53845 53672 53500 2.53329 53157 52986 52815 52645 2.52474 52304 52134 51965 51795 2.51626 51457 51289 51120 50952 2.50784 50617 50449 50282 50115 2.49948 49782 49616 49450 49284 2.49119 48954 48789 48624 48459 2.48295 48131 47967 47804 47640 2.47477 47314 47152 46989 46827 2.46665 46504 46342 46181 46020 2.45859 176 174 174 174 174 173 173 173 173 172 172 172 172 171 171 171 171 170 170 170 170 170 170 170 170 169 169 169 169 168 168 168 168 167 167 167 167 166 166 166 166 164 164 164 164 164 163 163 163 163 162 162 162 162 161 161 161 161 160 160 ➙ Diff 33 34 34 34 34 34 34 34 33 34 34 34 34 34 34 34 34 34 34 34 34 34 34 34 34 34 34 34 34 34 34 35 34 34 34 34 34 34 34 35 34 34 34 34 34 35 34 34 34 35 34 34 34 35 34 34 35 34 34 34 sec 113°➙ cos Diff 1′ sec Diff 1′ tan 0.42447 42482 42516 42551 42585 0.42619 42654 42688 42722 42757 0.42791 42826 42860 42894 42929 0.42963 42998 43032 43067 43101 0.43136 43170 43205 43239 43274 0.43308 43343 43378 43412 43447 0.43481 43516 43550 43585 43620 0.43654 43689 43724 43758 43793 0.43828 43862 43897 43932 43966 0.44001 44036 44071 44105 44140 0.44175 44210 44244 44279 44314 0.44349 44384 44418 44453 44488 0.44523 cot Diff 1′ 35 34 35 34 34 35 34 34 35 34 35 34 34 35 34 35 34 35 34 35 34 35 34 35 34 35 35 34 35 34 35 34 35 35 34 35 35 34 35 35 34 35 35 34 35 35 35 34 35 35 35 34 35 35 35 35 34 35 35 35 Diff 1′ cot 2.35585 35395 35205 35015 34825 2.34636 34447 34258 34069 33881 2.33693 33505 33317 33130 32943 2.32756 32570 32383 32197 32012 2.31826 31641 31456 31271 31086 2.30902 30718 30534 30351 30167 2.29984 29801 29619 29437 29254 2.29073 28891 28710 28528 28348 2.28167 27987 27806 27626 27447 2.27267 27088 26909 26730 26552 2.26374 26196 26018 25840 25663 2.25486 25309 25132 24956 24780 2.24604 tan Diff 1′ 190 190 190 190 190 190 189 189 189 189 188 188 188 188 187 187 187 187 186 186 186 186 184 184 184 184 183 183 183 183 182 182 182 182 181 181 181 181 180 180 180 180 180 180 180 180 179 179 179 179 179 178 178 178 178 177 177 177 177 176 Diff 1′ sec 1.08636 08649 08663 08676 08690 1.08703 08717 08730 08744 08757 1.08771 08784 08798 08811 08825 1.08839 08852 08866 08880 08893 1.08907 08920 08934 08948 08962 1.08975 08989 09003 09017 09030 1.09044 09058 09072 09086 09099 1.09113 09127 09141 09155 09169 1.09183 09197 09211 09224 09238 1.09252 09266 09280 09294 09308 1.09323 09337 09351 09365 09379 1.09393 09407 09421 09435 09449 1.09464 csc Diff 1′ 13 14 13 14 13 14 13 14 13 14 13 14 13 14 14 13 14 14 13 14 13 14 14 14 13 14 14 14 13 14 14 14 14 13 14 14 14 14 14 14 14 14 13 14 14 14 14 14 14 15 14 14 14 14 14 14 14 14 14 15 Diff 1′ cos 156° 0.92050 92039 92028 92016 92005 0.91994 91982 91971 91959 91948 0.91936 91925 91914 91902 91891 0.91879 91868 91856 91845 91833 0.91822 91810 91799 91787 91775 0.91764 91752 91741 91729 91718 0.91706 91694 91683 91671 91660 0.91648 91636 91625 91613 91601 0.91590 91578 91566 91555 91543 0.91531 91519 91508 91496 91484 0.91472 91461 91449 91437 91425 0.91414 91402 91390 91378 91366 0.91355 sin Diff 1′ 11 11 12 11 11 12 11 12 11 12 11 11 12 11 12 11 12 11 12 11 12 11 12 12 11 12 11 12 11 12 12 11 12 11 12 12 11 12 12 11 12 12 11 12 12 12 11 12 12 12 11 12 12 12 11 12 12 12 12 11 ′ 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 Diff ➙ cos 0.40403 40436 40470 40504 40538 0.40572 40606 40640 40674 40707 0.40741 40775 40809 40843 40877 0.40911 40945 40979 41013 41047 0.41081 41115 41149 41183 41217 0.41251 41285 41319 41353 41387 0.41421 41455 41490 41524 41558 0.41592 41626 41660 41694 41728 0.41763 41797 41831 41865 41899 0.41933 41968 42002 42036 42070 0.42105 42139 42173 42207 42242 0.42276 42310 42345 42379 42413 0.42447 Diff 1′ ➙ 192 191 191 191 190 190 190 190 190 190 190 189 189 189 188 188 188 188 187 187 187 186 186 186 186 184 184 184 183 183 183 183 182 182 182 181 181 181 181 180 180 180 180 180 180 180 179 179 179 179 178 178 178 178 177 177 177 177 176 176 ➙ 2.66947 66755 66563 66371 66180 2.65989 65799 65609 65419 65229 2.65040 64851 64662 64473 64285 2.64097 63909 63722 63535 63348 2.63162 62976 62790 62604 62419 2.62234 62049 61864 61680 61496 2.61313 61129 60946 60763 60581 2.60399 60217 60035 59853 59672 2.59491 59311 59130 58950 58771 2.58591 58412 58233 58054 57876 2.57698 57520 57342 57165 56988 2.56811 56634 56458 56282 56106 2.55930 cot ➙ 27 27 27 27 26 27 27 27 27 27 27 27 27 27 27 27 27 27 27 26 27 27 27 27 27 27 27 27 26 27 27 27 27 27 27 27 26 27 27 27 27 27 26 27 27 27 27 27 26 27 27 27 27 26 27 27 27 27 26 27 Diff 1′ 1′ 66° ➙ 112°➙ 157° ➙ 0.37461 37488 37515 37542 37569 0.37595 37622 37649 37676 37703 0.37730 37757 37784 37811 37838 0.37865 37892 37919 37946 37973 0.37999 38026 38053 38080 38107 0.38134 38161 38188 38215 38241 0.38268 38295 38322 38349 38376 0.38403 38430 38456 38483 38510 0.38537 38564 38591 38617 38644 0.38671 38698 38725 38752 38778 0.38805 38832 38859 38886 38912 0.38939 38966 38993 39020 39046 0.39073 tan ➙ Diff 1′ ➙ csc ➙ ➙ ′ 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 Diff 1′ ➙ 22°➙ sin 586 TABLE Natural Trigonometric Functions TABLE TABLE Natural Trigonometric Functions Natural Trigonometric Functions 1′ sec Diff 1′ cot Diff 1′ 3.48741 48359 47977 47596 47216 3.46837 46458 46080 45703 45327 3.44951 44576 44202 43829 43456 3.43084 42713 42343 41973 41604 3.41236 40869 40502 40136 39771 3.39406 39042 38679 38317 37955 3.37594 37234 36875 36516 36158 3.35800 35443 35087 34732 34377 3.34023 33670 33317 32965 32614 3.32264 31914 31565 31216 30868 3.30521 30174 29829 29483 29139 3.28795 28452 28109 27767 27426 3.27085 tan 382 381 380 380 380 379 378 378 377 376 374 374 373 372 371 371 370 370 369 369 368 367 366 366 364 363 363 362 361 360 360 360 359 359 358 357 357 356 354 353 353 352 351 351 350 350 350 349 348 348 347 346 346 344 343 343 342 341 341 340 Diff 1′ 1.04030 04039 04047 04056 04065 1.04073 04082 04091 04100 04108 1.04117 04126 04135 04144 04152 1.04161 04170 04179 04188 04197 1.04206 04214 04223 04232 04241 1.04250 04259 04268 04277 04286 1.04295 04304 04313 04322 04331 1.04340 04349 04358 04367 04376 1.04385 04394 04403 04413 04422 1.04431 04440 04449 04458 04468 1.04477 04486 04495 04504 04514 1.04523 04532 04541 04551 04560 1.04569 csc Diff 1′ 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 10 9 9 10 9 9 10 9 10 9 Diff 1′ cos 0.96126 96118 96110 96102 96094 0.96086 96078 96070 96062 96054 0.96046 96037 96029 96021 96013 0.96005 95997 95989 95981 95972 0.95964 95956 95948 95940 95931 0.95923 95915 95907 95898 95890 0.95882 95874 95865 95857 95849 0.95841 95832 95824 95816 95807 0.95799 95791 95782 95774 95766 0.95757 95749 95740 95732 95724 0.95715 95707 95698 95690 95681 0.95673 95664 95656 95647 95639 0.95630 sin Diff 1′ 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 9 8 9 9 9 ′ 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 Diff 1′ 73° 17°➙ ′ 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 sin Diff 1′ csc Diff 1′ 0.29237 29265 29293 29321 29348 0.29376 29404 29432 29460 29487 0.29515 29543 29571 29599 29626 0.29654 29682 29710 29737 29765 0.29793 29821 29849 29876 29904 0.29932 29960 29987 30015 30043 0.30071 30098 30126 30154 30182 0.30209 30237 30265 30292 30320 0.30348 30376 30403 30431 30459 0.30486 30514 30542 30570 30597 0.30625 30653 30680 30708 30736 0.30763 30791 30819 30846 30874 0.30902 28 28 28 27 28 28 28 28 27 28 28 28 28 27 28 28 28 27 28 28 28 28 27 28 28 28 27 28 28 28 27 28 28 28 27 28 28 27 28 28 28 27 28 28 27 28 28 28 27 28 28 27 28 28 27 28 28 27 28 28 3.42030 41705 41381 41057 40734 3.40411 40089 39768 39448 39128 3.38808 38489 38171 37854 37537 3.37221 36905 36590 36276 35962 3.35649 35336 35025 34713 34403 3.34092 33783 33474 33166 32858 3.32551 32244 31939 31633 31328 3.31024 30721 30418 30115 29814 3.29512 29212 28912 28612 28313 3.28015 27717 27420 27123 26827 3.26531 26237 25942 25648 25355 3.25062 24770 24478 24187 23897 3.23607 326 324 323 323 322 321 321 320 320 320 319 319 318 317 317 316 314 314 313 313 312 311 311 310 310 310 309 309 308 308 307 306 306 304 304 303 302 302 301 301 300 300 300 299 299 298 298 297 297 296 294 294 293 293 292 292 291 291 290 290 ➙ Diff 31 32 31 32 31 32 31 32 31 32 31 32 31 32 31 32 31 32 32 31 32 31 32 32 31 32 31 32 32 31 32 32 31 32 32 31 32 32 31 32 32 31 32 32 32 31 32 32 32 31 32 32 32 31 32 32 32 31 32 32 sec 107°➙ cos Diff 1′ sec Diff 1′ tan 0.30573 30605 30637 30669 30700 0.30732 30764 30796 30828 30860 0.30891 30923 30955 30987 31019 0.31051 31083 31115 31147 31178 0.31210 31242 31274 31306 31338 0.31370 31402 31434 31466 31498 0.31530 31562 31594 31626 31658 0.31690 31722 31754 31786 31818 0.31850 31882 31914 31946 31978 0.32010 32042 32074 32106 32139 0.32171 32203 32235 32267 32299 0.32331 32363 32396 32428 32460 0.32492 cot Diff 1′ 32 32 32 31 32 32 32 32 32 31 32 32 32 32 32 32 32 32 31 32 32 32 32 32 32 32 32 32 32 32 32 32 32 32 32 32 32 32 32 32 32 32 32 32 32 32 32 32 33 32 32 32 32 32 32 32 33 32 32 32 Diff 1′ cot 3.27085 26745 26406 26067 25729 3.25392 25055 24719 24383 24049 3.23714 23381 23048 22715 22384 3.22053 21722 21392 21063 20734 3.20406 20079 19752 19426 19100 3.18775 18451 18127 17804 17481 3.17159 16838 16517 16197 15877 3.15558 15240 14922 14605 14288 3.13972 13656 13341 13027 12713 3.12400 12087 11775 11464 11153 3.10842 10532 10223 09914 09606 3.09298 08991 08685 08379 08073 3.07768 tan Diff 1′ 340 340 339 339 338 337 337 336 334 334 333 332 332 331 331 330 330 330 329 329 328 327 327 326 324 324 323 323 322 321 321 320 320 320 320 319 318 318 317 317 316 314 314 313 313 312 312 311 310 310 310 310 309 309 308 308 307 306 306 304 Diff 1′ sec 1.04569 04578 04588 04597 04606 1.04616 04625 04635 04644 04653 1.04663 04672 04682 04691 04700 1.04710 04719 04729 04738 04748 1.04757 04767 04776 04786 04795 1.04805 04815 04824 04834 04843 1.04853 04863 04872 04882 04891 1.04901 04911 04920 04930 04940 1.04950 04959 04969 04979 04989 1.04998 05008 05018 05028 05038 1.05047 05057 05067 05077 05087 1.05097 05107 05116 05126 05136 1.05146 csc Diff 1′ 10 9 10 10 9 10 10 9 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 Diff 1′ cos 162° 0.95630 95622 95613 95605 95596 0.95588 95579 95571 95562 95554 0.95545 95536 95528 95519 95511 0.95502 95493 95485 95476 95467 0.95459 95450 95441 95433 95424 0.95415 95407 95398 95389 95380 0.95372 95363 95354 95345 95337 0.95328 95319 95310 95301 95293 0.95284 95275 95266 95257 95248 0.95240 95231 95222 95213 95204 0.95195 95186 95177 95168 95159 0.95150 95142 95133 95124 95115 0.95106 sin Diff 1′ 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 ′ 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 Diff ➙ cos 0.28675 28706 28738 28769 28801 0.28832 28864 28895 28927 28958 0.28990 29021 29053 29084 29116 0.29147 29179 29210 29242 29274 0.29305 29337 29368 29400 29432 0.29463 29495 29526 29558 29590 0.29621 29653 29685 29716 29748 0.29780 29811 29843 29875 29906 0.29938 29970 30001 30033 30065 0.30097 30128 30160 30192 30224 0.30255 30287 30319 30351 30382 0.30414 30446 30478 30509 30541 0.30573 Diff 1′ ➙ 368 367 367 366 364 363 363 362 361 360 360 360 359 358 358 357 356 354 354 353 352 351 351 350 350 349 349 348 347 347 346 344 343 343 342 341 341 340 340 340 339 338 338 337 336 336 334 333 333 332 331 331 330 330 330 329 328 328 327 326 ➙ 3.62796 62428 62061 61695 61330 3.60965 60601 60238 59876 59514 3.59154 58794 58434 58076 57718 3.57361 57005 56649 56294 55940 3.55587 55234 54883 54531 54181 3.53831 53482 53134 52787 52440 3.52094 51748 51404 51060 50716 3.50374 50032 49691 49350 49010 3.48671 48333 47995 47658 47321 3.46986 46651 46316 45983 45650 3.45317 44986 44655 44324 43995 3.43666 43337 43010 42683 42356 3.42030 cot ➙ 28 28 28 28 28 27 28 28 28 28 28 28 28 28 28 28 28 28 28 28 27 28 28 28 28 28 28 28 28 28 27 28 28 28 28 28 28 28 27 28 28 28 28 28 28 27 28 28 28 28 28 28 27 28 28 28 28 28 27 28 Diff 1′ 1′ 72° ➙ 0.27564 27592 27620 27648 27676 0.27704 27731 27759 27787 27815 0.27843 27871 27899 27927 27955 0.27983 28011 28039 28067 28095 0.28123 28150 28178 28206 28234 0.28262 28290 28318 28346 28374 0.28402 28429 28457 28485 28513 0.28541 28569 28597 28625 28652 0.28680 28708 28736 28764 28792 0.28820 28847 28875 28903 28931 0.28959 28987 29015 29042 29070 0.29098 29126 29154 29182 29209 0.29237 tan 583 106°➙ 163° ➙ Diff 1′ ➙ csc ➙ Diff 1′ ➙ ➙ ′ 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 sin ➙ 16°➙ TABLE Natural Trigonometric Functions 1′ sec Diff 1′ cot Diff 1′ 3.07768 07464 07160 06857 06554 3.06252 05950 05649 05349 05049 3.04749 04450 04152 03854 03556 3.03260 02963 02667 02372 02077 3.01783 01489 01196 00903 00611 3.00319 3.00028 2.99738 99447 99158 2.98868 98580 98292 98004 97717 2.97430 97144 96858 96573 96288 2.96004 95721 95437 95155 94872 2.94591 94309 94028 93748 93468 2.93189 92910 92632 92354 92076 2.91799 91523 91246 90971 90696 2.90421 tan 304 303 303 302 302 301 301 300 300 300 299 299 298 298 297 297 296 296 294 294 293 293 292 292 291 291 290 290 290 290 289 289 288 288 287 287 286 286 284 284 283 283 282 282 281 281 280 280 280 280 279 279 278 278 278 277 277 276 276 274 Diff 1′ 1.05146 05156 05166 05176 05186 1.05196 05206 05216 05226 05236 1.05246 05256 05266 05276 05286 1.05297 05307 05317 05327 05337 1.05347 05357 05367 05378 05388 1.05398 05408 05418 05429 05439 1.05449 05459 05470 05480 05490 1.05501 05511 05521 05532 05542 1.05552 05563 05573 05584 05594 1.05604 05615 05625 05636 05646 1.05657 05667 05678 05688 05699 1.05709 05720 05730 05741 05751 1.05762 csc Diff 1′ 10 10 10 10 10 10 10 10 10 10 10 10 10 10 11 10 10 10 10 10 10 10 11 10 10 10 10 11 10 10 10 11 10 10 11 10 10 11 10 10 11 10 11 10 10 11 10 11 10 11 10 11 10 11 10 11 10 11 10 11 Diff 1′ cos 0.95106 95097 95088 95079 95070 0.95061 95052 95043 95033 95024 0.95015 95006 94997 94988 94979 0.94970 94961 94952 94943 94933 0.94924 94915 94906 94897 94888 0.94878 94869 94860 94851 94842 0.94832 94823 94814 94805 94795 0.94786 94777 94768 94758 94749 0.94740 94730 94721 94712 94702 0.94693 94684 94674 94665 94656 0.94646 94637 94627 94618 94609 0.94599 94590 94580 94571 94561 0.94552 sin Diff 1′ 9 9 9 10 9 9 9 9 9 10 9 9 10 9 9 10 9 10 9 10 9 10 9 10 9 10 9 10 10 9 10 10 10 ′ 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 Diff 1′ 71° 19°➙ ′ 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 sin Diff 1′ csc Diff 1′ 0.32557 32584 32612 32639 32667 0.32694 32722 32749 32777 32804 0.32832 32859 32887 32914 32942 0.32969 32997 33024 33051 33079 0.33106 33134 33161 33189 33216 0.33244 33271 33298 33326 33353 0.33381 33408 33436 33463 33490 0.33518 33545 33573 33600 33627 0.33655 33682 33710 33737 33764 0.33792 33819 33846 33874 33901 0.33929 33956 33983 34011 34038 0.34065 34093 34120 34147 34175 0.34202 27 28 27 28 27 28 27 28 27 28 27 28 27 28 27 28 27 27 28 27 28 27 28 27 28 27 27 28 27 28 27 28 27 27 28 27 28 27 27 28 27 28 27 27 28 27 27 28 27 28 27 27 28 27 27 28 27 27 28 27 3.07155 06896 06637 06379 06121 3.05864 05607 05350 05094 04839 3.04584 04329 04075 03821 03568 3.03315 03062 02810 02559 02308 3.02057 01807 01557 01308 01059 3.00810 00562 00315 3.00067 2.99821 2.99574 99329 99083 98838 98594 2.98349 98106 97862 97619 97377 2.97135 96893 96652 96411 96171 2.95931 95691 95452 95213 94975 2.94737 94500 94263 94026 93790 2.93554 93318 93083 92849 92614 2.92380 260 259 259 258 258 257 257 257 256 256 254 254 253 253 252 252 251 251 251 250 250 250 250 249 249 249 248 248 247 247 246 246 246 244 244 243 243 242 242 242 241 241 240 240 240 240 240 239 239 238 238 238 237 237 236 236 236 234 234 233 ➙ Diff 32 32 32 33 32 32 32 32 33 32 32 32 33 32 32 32 33 32 32 32 33 32 32 33 32 32 33 32 32 33 32 32 33 32 32 33 32 32 33 32 33 32 33 32 32 33 32 33 32 33 32 33 32 33 32 33 32 33 32 33 sec 109°➙ cos Diff 1′ sec Diff 1′ tan 0.34433 34465 34498 34530 34563 0.34596 34628 34661 34693 34726 0.34758 34791 34824 34856 34889 0.34922 34954 34987 35020 35052 0.35085 35118 35150 35183 35216 0.35248 35281 35314 35346 35379 0.35412 35445 35477 35510 35543 0.35576 35608 35641 35674 35707 0.35740 35772 35805 35838 35871 0.35904 35937 35969 36002 36035 0.36068 36101 36134 36167 36199 0.36232 36265 36298 36331 36364 0.36397 cot Diff 1′ 32 33 32 33 33 32 33 32 33 32 33 33 32 33 33 32 33 33 32 33 33 32 33 33 32 33 33 32 33 33 33 32 33 33 33 32 33 33 33 33 32 33 33 33 33 33 32 33 33 33 33 33 33 32 33 33 33 33 33 33 Diff 1′ cot 2.90421 90147 89873 89600 89327 2.89055 88783 88511 88240 87970 2.87700 87430 87161 86892 86624 2.86356 86089 85822 85555 85289 2.85023 84758 84494 84229 83965 2.83702 83439 83176 82914 82653 2.82391 82130 81870 81610 81350 2.81091 80833 80574 80316 80059 2.79802 79545 79289 79033 78778 2.78523 78269 78014 77761 77507 2.77254 77002 76750 76498 76247 2.75996 75746 75496 75246 74997 2.74748 tan Diff 1′ 274 273 273 272 272 271 271 270 270 270 270 270 269 269 268 268 267 267 267 266 266 264 264 263 263 262 262 262 261 261 260 260 260 260 260 259 259 258 258 258 257 257 256 256 254 254 254 253 253 252 252 252 251 251 250 250 250 250 250 249 Diff 1′ sec 1.05762 05773 05783 05794 05805 1.05815 05826 05836 05847 05858 1.05869 05879 05890 05901 05911 1.05922 05933 05944 05955 05965 1.05976 05987 05998 06009 06020 1.06030 06041 06052 06063 06074 1.06085 06096 06107 06118 06129 1.06140 06151 06162 06173 06184 1.06195 06206 06217 06228 06239 1.06250 06261 06272 06283 06295 1.06306 06317 06328 06339 06350 1.06362 06373 06384 06395 06407 1.06418 csc Diff 1′ 11 10 11 11 10 11 10 11 11 11 10 11 11 10 11 11 11 11 10 11 11 11 11 11 10 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 12 11 11 11 11 11 12 11 11 11 12 11 Diff 1′ cos 160° 0.94552 94542 94533 94523 94514 0.94504 94495 94485 94476 94466 0.94457 94447 94438 94428 94418 0.94409 94399 94390 94380 94370 0.94361 94351 94342 94332 94322 0.94313 94303 94293 94284 94274 0.94264 94254 94245 94235 94225 0.94215 94206 94196 94186 94176 0.94167 94157 94147 94137 94127 0.94118 94108 94098 94088 94078 0.94068 94058 94049 94039 94029 0.94019 94009 93999 93989 93979 0.93969 sin Diff 1′ 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 ′ 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 Diff ➙ cos 0.32492 32524 32556 32588 32621 0.32653 32685 32717 32749 32782 0.32814 32846 32878 32911 32943 0.32975 33007 33040 33072 33104 0.33136 33169 33201 33233 33266 0.33298 33330 33363 33395 33427 0.33460 33492 33524 33557 33589 0.33621 33654 33686 33718 33751 0.33783 33816 33848 33881 33913 0.33945 33978 34010 34043 34075 0.34108 34140 34173 34205 34238 0.34270 34303 34335 34368 34400 0.34433 Diff 1′ ➙ 290 289 289 288 288 287 287 286 286 284 284 283 283 282 281 281 280 280 280 280 279 279 278 278 277 277 276 276 274 274 273 273 272 272 271 271 270 270 270 270 269 269 268 268 267 267 266 266 264 264 263 263 263 262 262 261 261 260 260 260 ➙ 3.23607 23317 23028 22740 22452 3.22165 21878 21592 21306 21021 3.20737 20453 20169 19886 19604 3.19322 19040 18759 18479 18199 3.17920 17641 17363 17085 16808 3.16531 16255 15979 15704 15429 3.15155 14881 14608 14335 14063 3.13791 13520 13249 12979 12709 3.12440 12171 11903 11635 11367 3.11101 10834 10568 10303 10038 3.09774 09510 09246 08983 08721 3.08459 08197 07936 07675 07415 3.07155 cot ➙ 27 28 28 27 28 28 27 28 28 27 28 27 28 28 27 28 28 27 28 27 28 28 27 28 28 27 28 27 28 27 28 28 27 28 27 28 27 28 28 27 28 27 28 27 28 27 28 28 27 28 27 28 27 28 27 28 27 28 27 28 Diff 1′ 1′ 70° ➙ 108°➙ 161° ➙ 0.30902 30929 30957 30985 31012 0.31040 31068 31095 31123 31151 0.31178 31206 31233 31261 31289 0.31316 31344 31372 31399 31427 0.31454 31482 31510 31537 31565 0.31593 31620 31648 31675 31703 0.31730 31758 31786 31813 31841 0.31868 31896 31923 31951 31979 0.32006 32034 32061 32089 32116 0.32144 32171 32199 32227 32254 0.32282 32309 32337 32364 32392 0.32419 32447 32474 32502 32529 0.32557 tan ➙ Diff 1′ ➙ csc ➙ ➙ ′ 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 Diff 1′ ➙ 18°➙ sin 584 TABLE Natural Trigonometric Functions TABLE TABLE Natural Trigonometric Functions Natural Trigonometric Functions 1′ sec Diff 1′ cot Diff 1′ 4.70463 69791 69121 68452 67786 4.67121 66458 65797 65138 64480 4.63825 63171 62518 61868 61219 4.60572 59927 59283 58641 58001 4.57363 56726 56091 55458 54826 4.54196 53568 52941 52316 51693 4.51071 50451 49832 49215 48600 4.47986 47374 46764 46155 45548 4.44942 44338 43735 43134 42534 4.41936 41340 40745 40152 39560 4.38969 38381 37793 37207 36623 4.36040 35459 34879 34300 33723 4.33148 tan 672 670 669 667 664 662 661 660 658 656 654 652 650 649 648 646 643 641 640 639 637 636 633 631 630 629 627 626 623 621 620 619 617 616 613 612 610 609 608 606 604 602 601 600 598 597 594 593 591 590 589 588 586 584 582 581 580 579 578 576 Diff 1′ 1.02234 02240 02247 02253 02259 1.02266 02272 02279 02285 02291 1.02298 02304 02311 02317 02323 1.02330 02336 02343 02349 02356 1.02362 02369 02375 02382 02388 1.02395 02402 02408 02415 02421 1.02428 02435 02441 02448 02454 1.02461 02468 02474 02481 02488 1.02494 02501 02508 02515 02521 1.02528 02535 02542 02548 02555 1.02562 02569 02576 02582 02589 1.02596 02603 02610 02617 02624 1.02630 csc Diff 1′ 6 7 6 7 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 Diff 1′ cos 0.97815 97809 97803 97797 97791 0.97784 97778 97772 97766 97760 0.97754 97748 97742 97735 97729 0.97723 97717 97711 97705 97698 0.97692 97686 97680 97673 97667 0.97661 97655 97648 97642 97636 0.97630 97623 97617 97611 97604 0.97598 97592 97585 97579 97573 0.97566 97560 97553 97547 97541 0.97534 97528 97521 97515 97508 0.97502 97496 97489 97483 97476 0.97470 97463 97457 97450 97444 0.97437 sin Diff 1′ 6 6 6 6 6 6 6 6 6 6 6 6 6 7 6 7 6 7 7 ′ 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 Diff 1′ 77° 13°➙ ′ 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 sin Diff 1′ csc Diff 1′ 0.22495 22523 22552 22580 22608 0.22637 22665 22693 22722 22750 0.22778 22807 22835 22863 22892 0.22920 22948 22977 23005 23033 0.23062 23090 23118 23146 23175 0.23203 23231 23260 23288 23316 0.23345 23373 23401 23429 23458 0.23486 23514 23542 23571 23599 0.23627 23656 23684 23712 23740 0.23769 23797 23825 23853 23882 0.23910 23938 23966 23995 24023 0.24051 24079 24108 24136 24164 0.24192 28 29 28 28 29 28 28 29 28 28 29 28 28 29 28 28 29 28 28 29 28 28 28 29 28 28 29 28 28 29 28 28 28 29 28 28 28 29 28 28 29 28 28 28 29 28 28 28 29 28 28 28 29 28 28 28 29 28 28 28 4.44541 43982 43424 42867 42312 4.41759 41206 40656 40106 39558 4.39012 38466 37923 37380 36839 4.36299 35761 35224 34689 34154 4.33622 33090 32560 32031 31503 4.30977 30452 29929 29406 28885 4.28366 27847 27330 26814 26300 4.25787 25275 24764 24255 23746 4.23239 22734 22229 21726 21224 4.20723 20224 19725 19228 18733 4.18238 17744 17252 16761 16271 4.15782 15295 14809 14323 13839 4.13357 560 558 557 556 553 552 550 550 548 547 546 543 542 541 540 539 537 536 534 532 531 530 529 528 527 524 523 522 520 520 519 518 516 514 513 511 510 510 509 507 506 504 503 501 500 500 499 498 496 494 493 492 491 490 489 488 487 486 484 482 ➙ Diff 30 30 31 30 31 30 31 30 30 31 30 31 30 31 30 31 30 31 30 30 31 30 31 30 31 30 31 30 31 30 31 31 30 31 30 31 30 31 30 31 30 31 31 30 31 30 31 30 31 31 30 31 30 31 31 30 31 31 30 31 sec 103°➙ cos Diff 1′ sec Diff 1′ tan 0.23087 23117 23148 23179 23209 0.23240 23271 23301 23332 23363 0.23393 23424 23455 23485 23516 0.23547 23578 23608 23639 23670 0.23700 23731 23762 23793 23823 0.23854 23885 23916 23946 23977 0.24008 24039 24069 24100 24131 0.24162 24193 24223 24254 24285 0.24316 24347 24377 24408 24439 0.24470 24501 24532 24562 24593 0.24624 24655 24686 24717 24747 0.24778 24809 24840 24871 24902 0.24933 cot Diff 1′ 30 31 31 30 31 31 30 31 31 30 31 31 30 31 31 31 30 31 31 30 31 31 31 30 31 31 31 30 31 31 31 30 31 31 31 31 30 31 31 31 31 30 31 31 31 31 31 30 31 31 31 31 31 30 31 31 31 31 31 31 Diff 1′ cot 4.33148 32573 32001 31430 30860 4.30291 29724 29159 28595 28032 4.27471 26911 26352 25795 25239 4.24685 24132 23580 23030 22481 4.21933 21387 20842 20298 19756 4.19215 18675 18137 17600 17064 4.16530 15997 15465 14934 14405 4.13877 13350 12825 12301 11778 4.11256 10736 10216 09699 09182 4.08666 08152 07639 07127 06616 4.06107 05599 05092 04586 04081 4.03578 03076 02574 02074 01576 4.01078 tan Diff 1′ 574 572 571 570 569 567 566 564 562 561 560 559 558 556 554 553 551 550 549 548 547 544 543 542 540 540 539 538 536 534 533 531 530 530 528 527 526 524 522 521 520 520 518 517 516 514 513 511 510 510 509 508 506 504 503 502 501 500 499 498 Diff 1′ sec 1.02630 02637 02644 02651 02658 1.02665 02672 02679 02686 02693 1.02700 02707 02714 02721 02728 1.02735 02742 02749 02756 02763 1.02770 02777 02784 02791 02799 1.02806 02813 02820 02827 02834 1.02842 02849 02856 02863 02870 1.02878 02885 02892 02899 02907 1.02914 02921 02928 02936 02943 1.02950 02958 02965 02972 02980 1.02987 02994 03002 03009 03017 1.03024 03032 03039 03046 03054 1.03061 csc Diff 1′ 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 8 7 Diff 1′ cos 166° 0.97437 97430 97424 97417 97411 0.97404 97398 97391 97384 97378 0.97371 97365 97358 97351 97345 0.97338 97331 97325 97318 97311 0.97304 97298 97291 97284 97278 0.97271 97264 97257 97251 97244 0.97237 97230 97223 97217 97210 0.97203 97196 97189 97182 97176 0.97169 97162 97155 97148 97141 0.97134 97127 97120 97113 97106 0.97100 97093 97086 97079 97072 0.97065 97058 97051 97044 97037 0.97030 sin Diff 1′ 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 ′ 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 Diff ➙ cos 0.21256 21286 21316 21347 21377 0.21408 21438 21469 21499 21529 0.21560 21590 21621 21651 21682 0.21712 21743 21773 21804 21834 0.21864 21895 21925 21956 21986 0.22017 22047 22078 22108 22139 0.22169 22200 22231 22261 22292 0.22322 22353 22383 22414 22444 0.22475 22505 22536 22567 22597 0.22628 22658 22689 22719 22750 0.22781 22811 22842 22872 22903 0.22934 22964 22995 23026 23056 0.23087 Diff 1′ ➙ 658 656 653 651 650 649 647 644 642 641 640 638 636 634 632 630 629 628 626 623 622 620 619 617 616 613 611 610 609 608 606 603 602 600 599 598 596 594 592 591 590 588 587 584 583 581 580 579 578 576 574 572 571 570 569 567 566 563 562 560 ➙ 4.80973 80316 79661 79007 78355 4.77705 77057 76411 75766 75123 4.74482 73843 73205 72569 71935 4.71303 70673 70044 69417 68791 4.68167 67545 66925 66307 65690 4.65074 64461 63849 63238 62630 4.62023 61417 60813 60211 59611 4.59012 58414 57819 57224 56632 4.56041 55451 54863 54277 53692 4.53109 52527 51947 51368 50791 4.50216 49642 49069 48498 47928 4.47360 46793 46228 45664 45102 4.44541 cot ➙ 29 28 29 28 28 29 28 29 28 29 28 28 29 28 29 28 29 28 28 29 28 29 28 29 28 28 29 28 29 28 28 29 28 29 28 28 29 28 28 29 28 29 28 28 29 28 28 29 28 29 28 28 29 28 28 29 28 28 29 28 Diff 1′ 1′ 76° ➙ 0.20791 20820 20848 20877 20905 0.20933 20962 20990 21019 21047 0.21076 21104 21132 21161 21189 0.21218 21246 21275 21303 21331 0.21360 21388 21417 21445 21474 0.21502 21530 21559 21587 21616 0.21644 21672 21701 21729 21758 0.21786 21814 21843 21871 21899 0.21928 21956 21985 22013 22041 0.22070 22098 22126 22155 22183 0.22212 22240 22268 22297 22325 0.22353 22382 22410 22438 22467 0.22495 tan 581 102°➙ 167° ➙ Diff 1′ ➙ csc ➙ Diff 1′ ➙ ➙ ′ 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 sin ➙ 12°➙ TABLE Natural Trigonometric Functions 1′ sec Diff 1′ cot Diff 1′ 4.01078 00582 4.00086 3.99592 99099 3.98607 98117 97627 97139 96651 3.96165 95680 95196 94713 94232 3.93751 93271 92793 92316 91839 3.91364 90890 90417 89945 89474 3.89004 88536 88068 87601 87136 3.86671 86208 85745 85284 84824 3.84364 83906 83449 82992 82537 3.82083 81630 81177 80726 80276 3.79827 79378 78931 78485 78040 3.77595 77152 76709 76268 75828 3.75388 74950 74512 74075 73640 3.73205 tan 497 496 494 492 491 490 490 489 488 487 486 483 482 481 480 480 479 478 477 476 474 473 471 470 470 469 468 467 466 464 463 462 461 460 460 459 458 457 456 454 453 452 451 450 450 449 448 447 446 444 443 442 441 440 440 439 438 437 436 434 Diff 1′ 1.03061 03069 03076 03084 03091 1.03099 03106 03114 03121 03129 1.03137 03144 03152 03159 03167 1.03175 03182 03190 03197 03205 1.03213 03220 03228 03236 03244 1.03251 03259 03267 03275 03282 1.03290 03298 03306 03313 03321 1.03329 03337 03345 03353 03360 1.03368 03376 03384 03392 03400 1.03408 03416 03424 03432 03439 1.03447 03455 03463 03471 03479 1.03487 03495 03503 03511 03520 1.03528 csc Diff 1′ 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 Diff 1′ cos 0.97030 97023 97015 97008 97001 0.96994 96987 96980 96973 96966 0.96959 96952 96945 96937 96930 0.96923 96916 96909 96902 96894 0.96887 96880 96873 96866 96858 0.96851 96844 96837 96829 96822 0.96815 96807 96800 96793 96786 0.96778 96771 96764 96756 96749 0.96742 96734 96727 96719 96712 0.96705 96697 96690 96682 96675 0.96667 96660 96653 96645 96638 0.96630 96623 96615 96608 96600 0.96593 sin Diff 1′ 7 7 7 7 7 7 7 7 7 7 7 7 7 7 8 7 8 7 8 8 ′ 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 Diff 1′ 75° 15°➙ ′ 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 sin Diff 1′ csc Diff 1′ 0.25882 25910 25938 25966 25994 0.26022 26050 26079 26107 26135 0.26163 26191 26219 26247 26275 0.26303 26331 26359 26387 26415 0.26443 26471 26500 26528 26556 0.26584 26612 26640 26668 26696 0.26724 26752 26780 26808 26836 0.26864 26892 26920 26948 26976 0.27004 27032 27060 27088 27116 0.27144 27172 27200 27228 27256 0.27284 27312 27340 27368 27396 0.27424 27452 27480 27508 27536 0.27564 28 28 28 28 28 28 29 28 28 28 28 28 28 28 28 28 28 28 28 28 28 29 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 3.86370 85951 85533 85116 84700 3.84285 83871 83457 83045 82633 3.82223 81813 81404 80996 80589 3.80183 79778 79374 78970 78568 3.78166 77765 77365 76966 76568 3.76171 75775 75379 74984 74591 3.74198 73806 73414 73024 72635 3.72246 71858 71471 71085 70700 3.70315 69931 69549 69167 68785 3.68405 68025 67647 67269 66892 3.66515 66140 65765 65391 65018 3.64645 64274 63903 63533 63164 3.62796 419 419 418 417 416 414 413 412 411 410 410 409 408 407 407 406 404 403 402 401 400 400 399 399 398 397 396 394 393 392 392 391 390 390 389 388 387 387 386 384 383 382 382 381 380 380 379 378 378 377 376 374 373 373 372 371 370 370 370 369 ➙ Diff 31 31 31 30 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 31 32 31 31 31 31 31 31 31 31 32 31 31 31 31 31 31 32 31 31 sec 105°➙ cos Diff 1′ sec Diff 1′ tan 0.26795 26826 26857 26888 26920 0.26951 26982 27013 27044 27076 0.27107 27138 27169 27201 27232 0.27263 27294 27326 27357 27388 0.27419 27451 27482 27513 27545 0.27576 27607 27638 27670 27701 0.27732 27764 27795 27826 27858 0.27889 27921 27952 27983 28015 0.28046 28077 28109 28140 28172 0.28203 28234 28266 28297 28329 0.28360 28391 28423 28454 28486 0.28517 28549 28580 28612 28643 0.28675 cot Diff 1′ 31 31 31 32 31 31 31 31 32 31 31 31 32 31 31 31 32 31 31 31 32 31 31 32 31 31 31 32 31 31 32 31 31 32 31 32 31 31 32 31 31 32 31 32 31 31 32 31 32 31 31 32 31 32 31 32 31 32 31 32 Diff 1′ cot 3.73205 72771 72338 71907 71476 3.71046 70616 70188 69761 69335 3.68909 68485 68061 67638 67217 3.66796 66376 65957 65538 65121 3.64705 64289 63874 63461 63048 3.62636 62224 61814 61405 60996 3.60588 60181 59775 59370 58966 3.58562 58160 57758 57357 56957 3.56557 56159 55761 55364 54968 3.54573 54179 53785 53393 53001 3.52609 52219 51829 51441 51053 3.50666 50279 49894 49509 49125 3.48741 tan Diff 1′ 433 432 431 430 430 430 429 428 427 426 424 423 422 421 420 420 420 419 418 417 416 414 413 412 412 411 410 410 409 408 407 407 406 404 403 402 401 400 400 400 399 398 397 397 396 394 393 392 391 391 390 390 389 388 388 387 386 384 384 383 Diff 1′ sec 1.03528 03536 03544 03552 03560 1.03568 03576 03584 03592 03601 1.03609 03617 03625 03633 03642 1.03650 03658 03666 03674 03683 1.03691 03699 03708 03716 03724 1.03732 03741 03749 03757 03766 1.03774 03783 03791 03799 03808 1.03816 03825 03833 03842 03850 1.03858 03867 03875 03884 03892 1.03901 03909 03918 03927 03935 1.03944 03952 03961 03969 03978 1.03987 03995 04004 04013 04021 1.04030 csc Diff 1′ 8 8 8 8 8 8 8 8 8 8 8 9 8 9 8 9 9 9 9 9 9 Diff 1′ cos 164° 0.96593 96585 96578 96570 96562 0.96555 96547 96540 96532 96524 0.96517 96509 96502 96494 96486 0.96479 96471 96463 96456 96448 0.96440 96433 96425 96417 96410 0.96402 96394 96386 96379 96371 0.96363 96355 96347 96340 96332 0.96324 96316 96308 96301 96293 0.96285 96277 96269 96261 96253 0.96246 96238 96230 96222 96214 0.96206 96198 96190 96182 96174 0.96166 96158 96150 96142 96134 0.96126 sin Diff 1′ 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 ′ 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 Diff ➙ cos 0.24933 24964 24995 25026 25056 0.25087 25118 25149 25180 25211 0.25242 25273 25304 25335 25366 0.25397 25428 25459 25490 25521 0.25552 25583 25614 25645 25676 0.25707 25738 25769 25800 25831 0.25862 25893 25924 25955 25986 0.26017 26048 26079 26110 26141 0.26172 26203 26235 26266 26297 0.26328 26359 26390 26421 26452 0.26483 26515 26546 26577 26608 0.26639 26670 26701 26733 26764 0.26795 Diff 1′ ➙ 481 480 480 479 478 476 474 473 472 471 470 470 469 467 466 464 463 462 461 460 460 459 458 457 456 453 452 451 450 450 449 448 447 446 444 443 442 441 440 440 439 438 437 436 434 433 432 431 430 430 429 428 427 426 424 423 422 421 420 420 ➙ 4.13357 12875 12394 11915 11437 4.10960 10484 10009 09535 09063 4.08591 08121 07652 07184 06717 4.06251 05786 05322 04860 04398 4.03938 03479 03020 02563 02107 4.01652 01198 00745 4.00293 3.99843 3.99393 98944 98497 98050 97604 3.97160 96716 96274 95832 95392 3.94952 94514 94076 93640 93204 3.92770 92337 91904 91473 91042 3.90613 90184 89756 89330 88904 3.88479 88056 87633 87211 86790 3.86370 cot ➙ 28 29 28 28 28 29 28 28 28 28 29 28 28 28 28 29 28 28 28 28 28 29 28 28 28 28 29 28 28 28 28 28 28 29 28 28 28 28 28 29 28 28 28 28 28 28 28 29 28 28 28 28 28 28 28 28 29 28 28 28 Diff 1′ 1′ 74° ➙ 104°➙ 165° ➙ 0.24192 24220 24249 24277 24305 0.24333 24362 24390 24418 24446 0.24474 24503 24531 24559 24587 0.24615 24644 24672 24700 24728 0.24756 24784 24813 24841 24869 0.24897 24925 24954 24982 25010 0.25038 25066 25094 25122 25151 0.25179 25207 25235 25263 25291 0.25320 25348 25376 25404 25432 0.25460 25488 25516 25545 25573 0.25601 25629 25657 25685 25713 0.25741 25769 25798 25826 25854 0.25882 tan ➙ Diff 1′ ➙ csc ➙ ➙ ′ 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 Diff 1′ ➙ 14°➙ sin 582 TABLE Natural Trigonometric Functions TABLE TABLE Natural Trigonometric Functions Natural Trigonometric Functions 1′ sec Diff 1′ cot Diff 1′ 7.11537 10038 08546 07059 05579 7.04105 02637 7.01174 6.99718 98268 6.96823 95385 93952 92525 91104 6.89688 88278 86874 85475 84082 6.82694 81312 79936 78564 77199 6.75838 74483 73133 71789 70450 6.69116 67787 66463 65144 63831 6.62523 61219 59921 58627 57339 6.56055 54777 53503 52234 50970 6.49710 48456 47206 45961 44720 6.43484 42253 41026 39804 38587 6.37374 36165 34961 33761 32566 6.31375 tan 1499 1492 1487 1480 1474 1469 1462 1457 1450 1444 1439 1432 1428 1421 1416 1410 1404 1399 1393 1388 1382 1377 1371 1366 1360 1356 1350 1344 1340 1334 1329 1323 1319 1313 1309 1303 1299 1293 1289 1283 1279 1273 1269 1264 1260 1254 1250 1246 1240 1236 1231 1227 1222 1218 1213 1209 1204 1200 1196 1190 Diff 1′ 1.00983 00987 00991 00995 00999 1.01004 01008 01012 01016 01020 1.01024 01029 01033 01037 01041 1.01046 01050 01054 01059 01063 1.01067 01071 01076 01080 01084 1.01089 01093 01097 01102 01106 1.01111 01115 01119 01124 01128 1.01133 01137 01142 01146 01151 1.01155 01160 01164 01169 01173 1.01178 01182 01187 01191 01196 1.01200 01205 01209 01214 01219 1.01223 01228 01233 01237 01242 1.01247 csc Diff 1′ 4 4 4 4 4 4 4 4 4 5 4 5 5 5 5 5 5 5 5 Diff 1′ cos 0.99027 99023 99019 99015 99011 0.99006 99002 98998 98994 98990 0.98986 98982 98978 98973 98969 0.98965 98961 98957 98953 98948 0.98944 98940 98936 98931 98927 0.98923 98919 98914 98910 98906 0.98902 98897 98893 98889 98884 0.98880 98876 98871 98867 98863 0.98858 98854 98849 98845 98841 0.98836 98832 98827 98823 98818 0.98814 98809 98805 98800 98796 0.98791 98787 98782 98778 98773 0.98769 sin Diff 1′ 4 4 4 4 4 4 4 4 4 4 4 4 4 5 4 5 5 5 5 ′ 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 Diff 1′ 81° 9°➙ ′ 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 sin Diff 1′ csc Diff 1′ 0.15643 15672 15701 15730 15758 0.15787 15816 15845 15873 15902 0.15931 15959 15988 16017 16046 0.16074 16103 16132 16160 16189 0.16218 16246 16275 16304 16333 0.16361 16390 16419 16447 16476 0.16505 16533 16562 16591 16620 0.16648 16677 16706 16734 16763 0.16792 16820 16849 16878 16906 0.16935 16964 16992 17021 17050 0.17078 17107 17136 17164 17193 0.17222 17250 17279 17308 17336 0.17365 29 29 29 28 29 29 29 28 29 29 28 29 29 29 28 29 29 28 29 29 28 29 29 29 28 29 29 28 29 29 28 29 29 29 28 29 29 28 29 29 28 29 29 28 29 29 28 29 29 28 29 29 28 29 29 28 29 29 28 29 6.39245 38073 36906 35743 34584 6.33429 32279 31133 29991 28853 6.27719 26590 25464 24343 23226 6.22113 21004 19898 18797 17700 6.16607 15517 14432 13350 12273 6.11199 10129 09062 08000 06941 6.05886 04834 03787 02743 01702 6.00666 5.99633 98603 97577 96555 5.95536 94521 93509 92501 91496 5.90495 89497 88502 87511 86524 5.85539 84558 83581 82606 81635 5.80667 79703 78742 77783 76829 5.75877 1171 1168 1163 1159 1154 1150 1147 1141 1138 1133 1130 1126 1121 1118 1113 1110 1106 1101 1098 1093 1090 1086 1081 1078 1073 1070 1067 1062 1059 1056 1051 1048 1043 1040 1037 1033 1030 1026 1022 1019 1016 1011 1009 1004 1001 998 994 991 988 984 981 978 974 971 968 964 961 959 954 951 ➙ Diff 30 29 30 30 29 30 30 29 30 30 30 29 30 30 29 30 30 29 30 30 30 29 30 30 29 30 30 30 29 30 30 30 29 30 30 30 29 30 30 30 29 30 30 30 29 30 30 30 30 29 30 30 30 30 29 30 30 30 30 29 sec 99°➙ cos Diff 1′ sec Diff 1′ tan 0.15838 15868 15898 15928 15958 0.15988 16017 16047 16077 16107 0.16137 16167 16196 16226 16256 0.16286 16316 16346 16376 16405 0.16435 16465 16495 16525 16555 0.16585 16615 16645 16674 16704 0.16734 16764 16794 16824 16854 0.16884 16914 16944 16974 17004 0.17033 17063 17093 17123 17153 0.17183 17213 17243 17273 17303 0.17333 17363 17393 17423 17453 0.17483 17513 17543 17573 17603 0.17633 cot Diff 1′ 30 30 30 30 30 29 30 30 30 30 30 29 30 30 30 30 30 30 29 30 30 30 30 30 30 30 30 29 30 30 30 30 30 30 30 30 30 30 30 29 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 Diff 1′ cot 6.31375 30189 29007 27829 26655 6.25486 24321 23160 22003 20851 6.19703 18559 17419 16283 15151 6.14023 12899 11779 10664 09552 6.08444 07340 06240 05143 04051 6.02962 01878 6.00797 5.99720 98646 5.97576 96510 95448 94390 93335 5.92283 91236 90191 89151 88114 5.87080 86051 85024 84001 82982 5.81966 80953 79944 78938 77936 5.76937 75941 74949 73960 72974 5.71992 71013 70037 69064 68094 5.67128 tan Diff 1′ 1187 1182 1178 1173 1170 1166 1160 1157 1152 1149 1144 1140 1136 1131 1128 1123 1120 1116 1111 1108 1104 1100 1097 1092 1089 1084 1080 1078 1073 1070 1066 1062 1059 1054 1051 1048 1044 1040 1037 1033 1030 1027 1022 1020 1017 1012 1010 1006 1002 1000 996 992 990 986 982 980 976 972 970 967 Diff 1′ sec 1.01247 01251 01256 01261 01265 1.01270 01275 01279 01284 01289 1.01294 01298 01303 01308 01313 1.01317 01322 01327 01332 01337 1.01342 01346 01351 01356 01361 1.01366 01371 01376 01381 01386 1.01391 01395 01400 01405 01410 1.01415 01420 01425 01430 01435 1.01440 01445 01450 01455 01460 1.01466 01471 01476 01481 01486 1.01491 01496 01501 01506 01512 1.01517 01522 01527 01532 01537 1.01543 csc Diff 1′ 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 Diff 1′ cos 170° 0.98769 98764 98760 98755 98751 0.98746 98741 98737 98732 98728 0.98723 98718 98714 98709 98704 0.98700 98695 98690 98686 98681 0.98676 98671 98667 98662 98657 0.98652 98648 98643 98638 98633 0.98629 98624 98619 98614 98609 0.98604 98600 98595 98590 98585 0.98580 98575 98570 98565 98561 0.98556 98551 98546 98541 98536 0.98531 98526 98521 98516 98511 0.98506 98501 98496 98491 98486 0.98481 sin Diff 1′ 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 ′ 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 Diff ➙ cos 0.14054 14084 14113 14143 14173 0.14202 14232 14262 14291 14321 0.14351 14381 14410 14440 14470 0.14499 14529 14559 14588 14618 0.14648 14678 14707 14737 14767 0.14796 14826 14856 14886 14915 0.14945 14975 15005 15034 15064 0.15094 15124 15153 15183 15213 0.15243 15272 15302 15332 15362 0.15391 15421 15451 15481 15511 0.15540 15570 15600 15630 15660 0.15689 15719 15749 15779 15809 0.15838 Diff 1′ ➙ 1484 1478 1471 1466 1460 1453 1448 1441 1436 1430 1423 1419 1412 1407 1400 1396 1390 1384 1379 1372 1368 1362 1357 1351 1346 1340 1336 1330 1324 1320 1314 1310 1303 1299 1293 1289 1283 1279 1273 1269 1264 1260 1254 1250 1244 1240 1236 1230 1226 1221 1217 1212 1208 1202 1199 1193 1190 1186 1180 1177 ➙ 7.18530 17046 15568 14096 12630 7.11171 09717 08269 06828 05392 7.03962 02538 7.01120 6.99708 98301 6.96900 95505 94115 92731 91352 6.89979 88612 87250 85893 84542 6.83196 81856 80521 79191 77866 6.76547 75233 73924 72620 71321 6.70027 68738 67454 66176 64902 6.63633 62369 61110 59855 58606 6.57361 56121 54886 53655 52429 6.51208 49991 48779 47572 46369 6.45171 43977 42787 41602 40422 6.39245 cot ➙ 29 29 29 29 28 29 29 29 29 28 29 29 29 28 29 29 29 29 28 29 29 29 29 28 29 29 29 28 29 29 29 28 29 29 29 29 28 29 29 29 28 29 29 29 28 29 29 29 28 29 29 29 28 29 29 29 28 29 29 28 Diff 1′ 1′ 80° ➙ 0.13917 13946 13975 14004 14033 0.14061 14090 14119 14148 14177 0.14205 14234 14263 14292 14320 0.14349 14378 14407 14436 14464 0.14493 14522 14551 14580 14608 0.14637 14666 14695 14723 14752 0.14781 14810 14838 14867 14896 0.14925 14954 14982 15011 15040 0.15069 15097 15126 15155 15184 0.15212 15241 15270 15299 15327 0.15356 15385 15414 15442 15471 0.15500 15529 15557 15586 15615 0.15643 tan 579 98°➙ 171° ➙ Diff 1′ ➙ csc ➙ Diff 1′ ➙ ➙ ′ 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 sin ➙ 8°➙ TABLE Natural Trigonometric Functions 1′ sec Diff 1′ cot Diff 1′ 5.67128 66165 65205 64248 63295 5.62344 61397 60452 59511 58573 5.57638 56706 55777 54851 53927 5.53007 52090 51176 50264 49356 5.48451 47548 46648 45751 44857 5.43966 43077 42192 41309 40429 5.39552 38677 37805 36936 36070 5.35206 34345 33487 32631 31778 5.30928 30080 29235 28393 27553 5.26715 25880 25048 24218 23391 5.22566 21744 20925 20107 19293 5.18480 17671 16863 16058 15256 5.14455 tan 963 960 957 953 950 948 944 941 939 936 932 930 927 923 920 918 914 911 909 906 902 900 897 894 891 889 886 882 880 878 874 871 870 867 863 860 859 856 853 850 848 846 842 840 838 834 832 830 828 824 822 820 818 814 812 810 808 804 802 800 Diff 1′ 1.01543 01548 01553 01558 01564 1.01569 01574 01579 01585 01590 1.01595 01601 01606 01611 01616 1.01622 01627 01633 01638 01643 1.01649 01654 01659 01665 01670 1.01676 01681 01687 01692 01698 1.01703 01709 01714 01720 01725 1.01731 01736 01742 01747 01753 1.01758 01764 01769 01775 01781 1.01786 01792 01798 01803 01809 1.01815 01820 01826 01832 01837 1.01843 01849 01854 01860 01866 1.01872 csc Diff 1′ 5 5 5 5 6 5 5 6 6 6 6 6 6 6 6 6 6 6 Diff 1′ cos 0.98481 98476 98471 98466 98461 0.98455 98450 98445 98440 98435 0.98430 98425 98420 98414 98409 0.98404 98399 98394 98389 98383 0.98378 98373 98368 98362 98357 0.98352 98347 98341 98336 98331 0.98325 98320 98315 98310 98304 0.98299 98294 98288 98283 98277 0.98272 98267 98261 98256 98250 0.98245 98240 98234 98229 98223 0.98218 98212 98207 98201 98196 0.98190 98185 98179 98174 98168 0.98163 sin Diff 1′ 5 5 5 5 5 5 5 5 5 5 5 5 6 5 6 5 6 6 6 ′ 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 Diff 1′ 79° 11°➙ ′ 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 sin Diff 1′ csc Diff 1′ 0.19081 19109 19138 19167 19195 0.19224 19252 19281 19309 19338 0.19366 19395 19423 19452 19481 0.19509 19538 19566 19595 19623 0.19652 19680 19709 19737 19766 0.19794 19823 19851 19880 19908 0.19937 19965 19994 20022 20051 0.20079 20108 20136 20165 20193 0.20222 20250 20279 20307 20336 0.20364 20393 20421 20450 20478 0.20507 20535 20563 20592 20620 0.20649 20677 20706 20734 20763 0.20791 28 29 29 28 29 28 29 28 29 28 29 28 29 29 28 29 28 29 28 29 28 29 28 29 28 29 28 29 28 29 28 29 28 29 28 29 28 29 28 29 28 29 28 29 28 29 28 29 28 29 28 28 29 28 29 28 29 28 29 28 5.24084 23301 22521 21742 20966 5.20193 19421 18652 17886 17121 5.16359 15599 14842 14087 13334 5.12583 11835 11088 10344 09602 5.08863 08125 07390 06657 05926 5.05197 04471 03746 03024 02303 5.01585 00869 5.00155 4.99443 98733 4.98025 97320 96616 95914 95215 4.94517 93821 93128 92436 91746 4.91058 90373 89689 89007 88327 4.87649 86973 86299 85627 84956 4.84288 83621 82956 82294 81633 4.80973 783 780 779 776 773 771 769 767 764 762 760 758 756 752 750 749 747 744 741 740 738 736 733 730 729 727 724 722 720 719 717 714 711 710 708 706 703 701 700 698 696 693 691 690 688 686 683 681 680 678 677 674 672 670 669 667 664 662 660 660 ➙ Diff 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 31 30 30 30 30 30 30 30 30 30 30 30 31 30 30 30 30 30 30 30 31 30 30 30 30 30 30 31 30 30 30 30 30 31 30 30 sec 101°➙ cos Diff 1′ sec Diff 1′ tan 0.19438 19468 19498 19529 19559 0.19589 19619 19649 19680 19710 0.19740 19770 19801 19831 19861 0.19891 19921 19952 19982 20012 0.20042 20073 20103 20133 20164 0.20194 20224 20254 20285 20315 0.20345 20376 20406 20436 20466 0.20497 20527 20557 20588 20618 0.20648 20679 20709 20739 20770 0.20800 20830 20861 20891 20921 0.20952 20982 21013 21043 21073 0.21104 21134 21164 21195 21225 0.21256 cot Diff 1′ 30 30 31 30 30 30 30 31 30 30 30 31 30 30 30 30 31 30 30 30 31 30 30 31 30 30 30 31 30 30 31 30 30 30 31 30 30 31 30 30 31 30 30 31 30 30 31 30 30 31 30 31 30 30 31 30 30 31 30 31 Diff 1′ cot 5.14455 13658 12862 12069 11279 5.10490 09704 08921 08139 07360 5.06584 05809 05037 04267 03499 5.02734 01971 01210 5.00451 4.99695 4.98940 98188 97438 96690 95945 4.95201 94460 93721 92984 92249 4.91516 90785 90056 89330 88605 4.87882 87162 86444 85727 85013 4.84300 83590 82882 82175 81471 4.80769 80068 79370 78673 77978 4.77286 76595 75906 75219 74534 4.73851 73170 72490 71813 71137 4.70463 tan Diff 1′ 798 796 793 790 789 786 783 781 780 777 774 772 770 768 766 763 760 759 757 754 752 750 748 746 743 741 740 738 734 732 730 729 727 724 722 720 719 717 714 712 710 709 707 704 702 700 699 697 694 692 690 689 687 686 683 681 680 678 676 673 Diff 1′ sec 1.01872 01877 01883 01889 01895 1.01901 01906 01912 01918 01924 1.01930 01936 01941 01947 01953 1.01959 01965 01971 01977 01983 1.01989 01995 02001 02007 02013 1.02019 02025 02031 02037 02043 1.02049 02055 02061 02067 02073 1.02079 02085 02091 02097 02103 1.02110 02116 02122 02128 02134 1.02140 02146 02153 02159 02165 1.02171 02178 02184 02190 02196 1.02203 02209 02215 02221 02228 1.02234 csc Diff 1′ 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 Diff 1′ cos 168° 0.98163 98157 98152 98146 98140 0.98135 98129 98124 98118 98112 0.98107 98101 98096 98090 98084 0.98079 98073 98067 98061 98056 0.98050 98044 98039 98033 98027 0.98021 98016 98010 98004 97998 0.97992 97987 97981 97975 97969 0.97963 97958 97952 97946 97940 0.97934 97928 97922 97916 97910 0.97905 97899 97893 97887 97881 0.97875 97869 97863 97857 97851 0.97845 97839 97833 97827 97821 0.97815 sin Diff 1′ 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 ′ 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 Diff ➙ cos 0.17633 17663 17693 17723 17753 0.17783 17813 17843 17873 17903 0.17933 17963 17993 18023 18053 0.18083 18113 18143 18173 18203 0.18233 18263 18293 18323 18353 0.18384 18414 18444 18474 18504 0.18534 18564 18594 18624 18654 0.18684 18714 18745 18775 18805 0.18835 18865 18895 18925 18955 0.18986 19016 19046 19076 19106 0.19136 19166 19197 19227 19257 0.19287 19317 19347 19378 19408 0.19438 Diff 1′ ➙ 949 946 942 939 936 932 930 927 923 920 918 914 911 909 906 902 900 897 893 890 888 886 882 880 877 873 870 869 866 862 860 858 854 851 850 847 843 840 839 836 833 830 828 826 822 820 818 816 812 810 808 806 802 800 798 796 792 790 788 786 ➙ 5.75877 74929 73983 73041 72102 5.71166 70234 69304 68377 67454 5.66533 65616 64701 63790 62881 5.61976 61073 60174 59277 58383 5.57493 56605 55720 54837 53958 5.53081 52208 51337 50468 49603 5.48740 47881 47023 46169 45317 5.44468 43622 42778 41937 41099 5.40263 39430 38600 37772 36947 5.36124 35304 34486 33671 32859 5.32049 31241 30436 29634 28833 5.28036 27241 26448 25658 24870 5.24084 cot ➙ 28 29 29 28 29 29 28 29 29 28 29 28 29 29 28 29 29 28 29 28 29 29 28 29 29 28 29 28 29 29 28 29 28 29 29 28 29 28 29 28 29 29 28 29 28 29 29 28 29 28 29 28 29 29 28 29 28 29 28 29 Diff 1′ 1′ 78° ➙ 100°➙ 169° ➙ 0.17365 17393 17422 17451 17479 0.17508 17537 17565 17594 17623 0.17651 17680 17708 17737 17766 0.17794 17823 17852 17880 17909 0.17937 17966 17995 18023 18052 0.18081 18109 18138 18166 18195 0.18224 18252 18281 18309 18338 0.18367 18395 18424 18452 18481 0.18509 18538 18567 18595 18624 0.18652 18681 18710 18738 18767 0.18795 18824 18852 18881 18910 0.18938 18967 18995 19024 19052 0.19081 tan ➙ Diff 1′ ➙ csc ➙ ➙ ′ 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 Diff 1′ ➙ 10°➙ sin 580 TABLE Natural Trigonometric Functions TABLE Natural Trigonometric Functions 44°➙ 21 21 21 20 21 21 21 21 21 21 21 21 20 21 21 21 21 21 20 21 21 21 21 20 21 21 21 20 21 21 21 20 21 21 21 20 21 21 20 21 21 20 21 21 20 21 21 20 21 21 20 21 21 20 21 20 21 21 20 21 1.43956 43912 43869 43826 43783 1.43739 43696 43653 43610 43567 1.43524 43481 43438 43395 43352 1.43309 43267 43224 43181 43139 1.43096 43053 43011 42968 42926 1.42883 42841 42799 42756 42714 1.42672 42630 42587 42545 42503 1.42461 42419 42377 42335 42293 1.42251 42209 42168 42126 42084 1.42042 42001 41959 41918 41876 1.41835 41793 41752 41710 41669 1.41627 41586 41545 41504 41463 1.41421 43 43 43 43 43 43 43 43 43 43 42 42 42 42 42 42 42 42 42 42 42 42 42 42 42 42 42 42 42 42 42 42 42 42 42 42 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 41 cos Diff 1′ sec Diff 1′ tan 0.96569 96625 96681 96738 96794 0.96850 96907 96963 97020 97076 0.97133 97189 97246 97302 97359 0.97416 97472 97529 97586 97643 0.97700 97756 97813 97870 97927 0.97984 98041 98098 98155 98213 0.98270 98327 98384 98441 98499 0.98556 98613 98671 98728 98786 0.98843 98901 98958 99016 99073 0.99131 99189 99247 99304 99362 0.99420 99478 99536 99594 99652 0.99710 99768 99826 99884 99942 1.00000 cot Diff 1′ 56 56 57 56 56 57 56 57 56 57 56 57 56 57 57 56 57 57 57 57 56 57 57 57 57 57 57 57 58 57 57 57 57 58 57 57 58 57 58 57 58 57 58 57 58 58 58 57 58 58 58 58 58 58 58 58 58 58 58 58 Diff 1′ cot 1.03553 03493 03433 03372 03312 1.03252 03192 03132 03072 03012 1.02952 02892 02832 02772 02713 1.02653 02593 02533 02474 02414 1.02355 02295 02236 02176 02117 1.02057 01998 01939 01879 01820 1.01761 01702 01642 01583 01524 1.01465 01406 01347 01288 01229 1.01170 01112 01053 00994 00935 1.00876 00818 00759 00701 00642 1.00583 00525 00467 00408 00350 1.00291 00233 00175 00116 00058 1.00000 tan Diff 1′ 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 59 59 59 59 59 59 59 59 59 59 59 59 59 59 59 59 59 59 59 59 59 59 59 59 Diff 1′ sec 1.39016 39055 39095 39134 39173 1.39212 39251 39291 39330 39369 1.39409 39448 39487 39527 39566 1.39606 39646 39685 39725 39764 1.39804 39844 39884 39924 39963 1.40003 40043 40083 40123 40163 1.40203 40243 40283 40324 40364 1.40404 40444 40485 40525 40565 1.40606 40646 40687 40727 40768 1.40808 40849 40890 40930 40971 1.41012 41053 41093 41134 41175 1.41216 41257 41298 41339 41380 1.41421 csc Diff 1′ 39 40 39 39 39 39 40 39 39 40 39 39 40 39 40 40 39 40 39 40 40 40 40 39 40 40 40 40 40 40 40 40 41 40 40 40 41 40 40 41 40 41 40 41 40 41 41 40 41 41 41 40 41 41 41 41 41 41 41 41 Diff 1′ cos 0.71934 71914 71894 71873 71853 0.71833 71813 71792 71772 71752 0.71732 71711 71691 71671 71650 0.71630 71610 71590 71569 71549 0.71529 71508 71488 71468 71447 0.71427 71407 71386 71366 71345 0.71325 71305 71284 71264 71243 0.71223 71203 71182 71162 71141 0.71121 71100 71080 71059 71039 0.71019 70998 70978 70957 70937 0.70916 70896 70875 70855 70834 0.70813 70793 70772 70752 70731 0.70711 sin Diff 1′ 20 20 21 20 20 20 21 20 20 20 21 20 20 21 20 20 20 21 20 20 21 20 20 21 20 20 21 20 21 20 20 21 20 21 20 20 21 20 21 20 21 20 21 20 20 21 20 21 20 21 20 21 20 21 21 20 21 20 21 20 ′ 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 Diff ➙ 0.69466 69487 69508 69529 69549 0.69570 69591 69612 69633 69654 0.69675 69696 69717 69737 69758 0.69779 69800 69821 69842 69862 0.69883 69904 69925 69946 69966 0.69987 70008 70029 70049 70070 0.70091 70112 70132 70153 70174 0.70195 70215 70236 70257 70277 0.70298 70319 70339 70360 70381 0.70401 70422 70443 70463 70484 0.70505 70525 70546 70567 70587 0.70608 70628 70649 70670 70690 0.70711 ➙ Diff 1′ 1′ 45° ➙ csc 597 134°➙ 135° ➙ Diff 1′ ➙ ➙ ′ 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 sin [...]... 0. 520 02 520 26 520 51 520 76 521 01 0. 521 26 521 51 521 75 522 00 522 25 0. 522 50 522 75 522 99 523 24 523 49 0. 523 74 523 99 524 23 524 48 524 73 0. 524 98 525 22 525 47 525 72 525 97 0. 526 21 526 46 526 71 526 96 527 20 0. 527 45 527 70 527 94 528 19 528 44 0. 528 69 528 93 529 18 529 43 529 67 0. 529 92 25 25 25 25 24 25 25 25 25 25 25 25 25 24 25 25 25 25 25 25 24 25 25 25 25 25 24 25 25 25 25 24 25 25 25 25 24 25 25 25 24 25 25 25 24 25 25 ... 28 28 28 28 27 28 28 28 28 28 28 28 28 28 28 28 28 28 28 27 28 28 28 28 28 28 28 28 28 27 28 28 28 28 28 28 28 27 28 28 28 28 28 28 27 28 28 28 28 28 28 27 28 28 28 28 28 27 28 Diff 1′ 1′ 72 ➙ 0 .27 564 27 5 92 27 620 27 648 27 676 0 .27 704 27 731 27 759 27 787 27 815 0 .27 843 27 871 27 899 27 927 27 955 0 .27 983 28 011 28 039 28 067 28 095 0 .28 123 28 150 28 178 28 206 28 234 0 .28 2 62 2 829 0 28 318 28 346 28 374 0 .28 4 02 28 429 28 457... 2. 47509 tan Diff 1′ 22 7 22 6 22 6 22 6 22 4 22 4 22 4 22 3 22 3 22 3 22 2 22 2 22 2 22 1 22 1 22 1 22 0 22 0 22 0 22 0 22 0 22 0 21 9 21 9 21 9 21 9 21 8 21 8 21 8 21 7 21 7 21 7 21 6 21 6 21 6 21 4 21 4 21 4 21 3 21 3 21 3 21 2 21 2 21 2 21 1 21 1 21 1 21 1 21 0 21 0 21 0 21 0 21 0 21 0 20 9 20 9 20 9 20 9 20 8 20 8 Diff 1′ sec 1.07114 07 126 07138 07150 071 62 1.07174 07186 07199 0 721 1 0 722 3 1.0 723 5 0 724 7 0 725 9 0 727 1 0 728 3 1.0 729 5 07307 07 320 073 32 07344 1.07356... 22 665 22 693 22 722 22 750 0 .22 778 22 807 22 835 22 863 22 8 92 0 .22 920 22 948 22 977 23 005 23 033 0 .23 0 62 23090 23 118 23 146 23 175 0 .23 203 23 231 23 260 23 288 23 316 0 .23 345 23 373 23 401 23 429 23 458 0 .23 486 23 514 23 5 42 23571 23 599 0 .23 627 23 656 23 684 23 7 12 23740 0 .23 769 23 797 23 825 23 853 23 8 82 0 .23 910 23 938 23 966 23 995 24 023 0 .24 051 24 079 24 108 24 136 24 164 0 .24 1 92 28 29 28 28 29 28 28 29 28 28 29 28 28 29 28 28 29 ... 27 845 27 710 27 574 2. 27439 27 304 27 169 27 035 26 900 2. 26766 26 6 32 26498 26 364 26 230 2. 26097 25 963 25 830 25 697 25 565 2. 254 32 25300 25 167 25 035 24 903 2. 247 72 24640 24 509 24 378 24 247 2. 24116 23 985 23 855 23 724 23 594 2. 23464 23 334 23 205 23 075 22 946 2. 228 17 22 688 22 559 22 430 22 3 02 2 .22 174 22 045 21 918 21 790 21 6 62 2 .21 535 21 407 21 280 21 153 21 026 2. 20900 20 773 20 647 20 521 20 395 2. 2 026 9 cot ➙ 26 26 27 26 26 26 26 26 ... 23 1 23 0 23 0 23 0 23 0 23 0 22 9 22 9 22 9 22 8 22 8 22 7 22 7 22 7 22 6 22 6 22 4 22 4 22 4 22 3 22 3 22 3 22 2 22 2 22 1 22 1 22 1 22 0 22 0 22 0 22 0 22 0 22 0 21 9 21 9 21 8 21 8 21 8 21 7 21 7 21 7 21 6 21 6 21 6 21 4 21 4 21 4 21 3 21 3 21 3 21 2 21 2 21 1 21 1 ➙ 2. 923 80 921 47 91914 91681 91449 2. 9 121 7 90986 90754 90 524 9 029 3 2. 90063 89834 89605 89376 89148 2. 88 920 886 92 88465 8 823 8 88011 2. 87785 87560 87334 87109 86885 2. 86661 86437 8 621 3 85990... 28 28 29 28 28 28 28 28 28 29 28 28 28 28 28 29 28 28 28 28 28 28 28 29 28 28 28 28 28 28 28 28 29 28 28 28 Diff 1′ 1′ 74° ➙ 104°➙ 165° ➙ 0 .24 1 92 2 422 0 24 249 24 277 24 305 0 .24 333 24 3 62 24390 24 418 24 446 0 .24 474 24 503 24 531 24 559 24 587 0 .24 615 24 644 24 6 72 24700 24 728 0 .24 756 24 784 24 813 24 841 24 869 0 .24 897 24 925 24 954 24 9 82 25010 0 .25 038 25 066 25 094 25 122 25 151 0 .25 179 25 207 25 235 25 263 25 291 0 .25 320 25 348... 0 .26 022 26 050 26 079 26 107 26 135 0 .26 163 26 191 26 219 26 247 26 275 0 .26 303 26 331 26 359 26 387 26 415 0 .26 443 26 471 26 500 26 528 26 556 0 .26 584 26 6 12 26640 26 668 26 696 0 .26 724 26 7 52 26780 26 808 26 836 0 .26 864 26 8 92 26 920 26 948 26 976 0 .27 004 27 0 32 27060 27 088 27 116 0 .27 144 27 1 72 2 720 0 27 228 27 256 0 .27 284 27 3 12 27340 27 368 27 396 0 .27 424 27 4 52 27480 27 508 27 536 0 .27 564 28 28 28 28 28 28 29 28 28 28 28 28 28 28 28 28 ... 29 28 29 28 28 29 28 29 28 28 29 28 29 28 28 29 28 28 29 28 29 28 28 29 28 28 29 28 29 28 28 29 28 28 29 28 28 29 28 Diff 1′ 1′ 76° ➙ 0 .20 791 20 820 20 848 20 877 20 905 0 .20 933 20 9 62 20990 21 019 21 047 0 .21 076 21 104 21 1 32 21161 21 189 0 .21 218 21 246 21 275 21 303 21 331 0 .21 360 21 388 21 417 21 445 21 474 0 .21 5 02 21530 21 559 21 587 21 616 0 .21 644 21 6 72 21701 21 729 21 758 0 .21 786 21 814 21 843 21 871 21 899 0 .21 928 21 956... 31 722 31754 31786 31818 0.31850 318 82 31914 31946 31978 0. 320 10 320 42 320 74 321 06 321 39 0. 321 71 322 03 322 35 322 67 322 99 0. 323 31 323 63 323 96 324 28 324 60 0. 324 92 cot Diff 1′ 32 32 32 31 32 32 32 32 32 31 32 32 32 32 32 32 32 32 31 32 32 32 32 32 32 32 32 32 32 32 32 32 32 32 32 32 32 32 32 32 32 32 32 32 32 32 32 32 33 32 32 32 32 32 32 32 33 32 32 32 Diff 1′ cot 3 .27 085 26 745 26 406 26 067 25 729 3 .25 392

the american practical navigator table 2 natural trigonometric functions

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