TRAN VINH TAP MOT NHA XUAT BAN HA NOI TRAN VINH ^ ^ > THIET KE BAI GIANG DAI SO VA GIAI TICH /\ /\ NANG CAO - TAP MOT NHA XUAT BAN HA NO! Thiet kebai giang OAI SO VA GIAI TICH 11 - TAP MOT, NANG CAO TRAN VINH N H A XUAT BAN H A N O I Chiu trdch nhiem xudt bdn: NGUYfiN K H A C O A N H Bien tap: PHAM QUOC TUAN Vebia: NGUYfiN T U X N Trinh bdy: THAI SON - SON LAM Svta bdn in: PHAM QUOC TUAN In 1.000 cuon khd 17 x 24 cm tai Cong ty TNHH Bao bi va In Hai Nam Quyet dinh xuat ban so: 127 - 2008/CXB/100'= TK - 05/HN In xong va nop liiu chieu quy III nam 2O08 J^ai noi adu Trong nhi5ng nam gin day, thuc hidn ddi mdi chuefng trinh Sach giao khoa (SGK) cua Bo Giao duo va Dao tao, b6 SGK mdri dcfi, co b6 sach bien scan theo chuong trinh phan ban cua bac Trung hoc thong Bo sach gom ba ban: Ban co ban Ban nang cao khoa hoc tu nhien va Ban nang cao khoa hoc xa hoi Viec bo sach SGK m6i ddng nghia vdi vi6c phai ddi m6i phuong phap day va hoc Nham dap img nhiing yeu cSu do, tiep ndi bo sach: ThiSt k6' bai giang m6n toan ldp 10, chiing toi tiep tuc bien scan bo sach: Thiet ke bai giang mon Toan ldp 11 Bg sach gom, cuon: Thiet kebdi gidng Hinh hoc 11:2 tap Thiei kebdi gidng Dgi sdvd Gidi tich 11:2 tap Thiit kebdi gidng Hinh hoc 11 ndng cao: tap Thiit kebdi gidng Dgi sdvd Gidi tich 11 ndng cao: tap Day la b6 sach co nhieu hudng thiet ke, co nhieu dang, nhieu loai cau hoi, bai tap nham hudng hoc sinh (HS) den nhung don vi kien thiic nha't dinh He thdng cac cau hoi trac nghiem khach quan d cudi bai nham giup HS on tap va nang cao ki nang phan doan, quy nap, tijr dd xac dinh duoc noi dung kidn thiic chu yeu va co ban ciia bai hoc Bo sach duoc cac tac gia cd nhieu kinh nghiem giang day, nghien cuu khoa hoc (dac biet cd nhieu tac gia da nghien ciiu nhung phSn mem de hd tro giang day, nha't la cac mdn hoc khoa hoc tu nhifen, toan hoc ) Bien soan bg sach ddi hy vong giiip ban doc cd mdt each nhin mdi, phucmg phap mdi Cac each thiet ke bo sach vtta cd tmh dinh hudng, vita cu the, nham tao cac hudng md de giao vien (GV) ap dung ddi vdi nhiing ddi tugng HS khac Tuy da nghien ciiu va bien scan cin than, soiig khdng the tranh nhiing sai sdt, tac gia kfnh mong dugc su gdp y ciia ban dgc TAC GIA CHlTdNG I HAM SO Ll/dNG GIAC • VA PHlTdNG TRINH LlTdNG GIAC ^ • PHan ^sHwf^G TAX: n& CUA cm/di^G I NOI DUNG Ngi dung chinh cua chuefng 1: Ham sd lugng giac : Tinh tuSn hoan, su bien thien cua cac ham sd y = sinx, y = cosx, y = tanx va y = cotx Phucfng trinh lugng giac co ban : Cdng thiic nghiem va didu kien cd nghiem cua cac phucfng trinh sinx = m, cosx = m, tanx = m va cotx = m Dac biet la chii y de'n cac phuofng trinh sinx = sin a, cosx = cosa, tanx = tana va cotx = cota Mgt sd phucfng trinh lugng giac thudng gap: Phuong trinh dua ve bac nh&, bac hai ddi vdi cac ham sd lugng giac; Phucfng trinh bac nhit ddi vdi sinx va cosx, phucmg trinh thuan nhat bac hai ddi vdi sinx va cosx va mgt sd dang phuong trinh khac II MUCTIEU Kien thurc Nam dugc toan bd kien thiic co ban chucmg da neu tren, cu the : Hieu khai niem, chieu bie'n thien, tinh tudn hoan cua cac ham sd lugng giac Ap dung chieu bien thien va tinh tuan hoan ciia cac ham sd lugng giac de giai dugc cac phucmg trinh lugng giac Nam dugc cac cdng thiic nghiem dl giai cac phuong trinh lugng giac ccf ban Hilu each tim nghiem cua cac phuong trinh lugng giac ccf ban va phuomg phap giai mdt sd dang phucmg trinh lugng giac don gian Nam dugc mdt sd phuomg phap giai mdt sd dang phucmg trinh lugng giac khac Hieu khai niem cac ham sd lugng giac y =sinx, y = cosx, y = tanx, y = cot X va tinh chat tuSn hoan cua chung Nam dugc su bie'n thien va hinh dang dd thi cua cac ham sd lugng giac neu tren KT nang Sit dung thao cdng thiic nghiem Giai thao cac phucmg trinh lugng giac cof ban va mdt sd dang phucmg trinh lugng giac khac Bie't xet su bie'n thien, ve dd thi cua cac ham sd lugng giac y — siiu, y = cosx, y = tan X, y = cot x va mgt sd ham sd lugng giac dofn gian khac Giai thao cac phucmg trinh lugng giac ca ban Bie't each giai mgt sd dang phucmg trinh lugng giac khdng qua phiic tap cd the quy dugc ve phucmg trinh bac nhit va bac hai dd'i vdi mdt ham sd lucmg giac Thai Tu giac, tich cue, ddc lap va chu ddng phat hien cung nhu linh hdi kie'n thiic qua trinh hoat ddng cdn than, chinh xac lap luan va tinh toan Cam nhan dugc thuc te' cua toan hge, nh^t la ddi vdi lugng giac III CAU TAO C O A C H U O N G Du kie'n thuc hien 17 tiet, phan phdi cu thi nhu sau : § Cac ham sd lugng giac (3 tie't) Luyen tap (1 tie't) §2 Phucmg trinh lugng giac cor ban (3 tiet) Luyen tap (2 tiet) §3 Mdt sd dang phuomg trinh lugng giac dom gian (4 tiet) Luyen tap (2 tiet) On tap va kiem tra chuomg (2 tie't) IV NHQNG DIEU CAN LUU Y TRONG CHUONG 1) Trudc day, toan bd vin de lugng giac nam chucmg trinh Dai sd va Giai tfch 11 Trong chuomg trinh mdi, phin md diu ve lugng giac da dugc gidi thieu d chucmg cudi cua Dai sd 10, bao gdm cac van dd xay dung cac khai niem ccf ban nhu gdc va cung lugng giac, cac gia tri lugmg giac cua gdc (cung) lugng giac va mgt sd cdng thiic lugng giac Lugmg giac ldp 11 la su ndi tie'p chucmg trinh lugmg giac ldp 10 Dac diem dd ddi hdi giao vien phai luu y nhae lai hay ggi md cho hge sinh nhd lai cac kidn thiic d ldp 10 cd lien quan den bai hoc de de dang tiep thu kien thiic mdi 2) O ldp 10 chi ndi den cac gid tri lugng giac ciia gdc hay cung lugng giac a Sang ldp 11, ndi den cac ham sd lugng giac y =sinx, y = cosx, y = tan X, y = cotx ta hieu x la sd thuc va la sd radian cua gdc hay cung lugng giac 3) Day la lan dau tien hge sinh lam quen vdi ham sd tuin hoan Tuin hoan la tfnh cha^t ndi bat cua cac ham sd lugng giac nen mac dii chuomg trinh khdng yeu cau trinh bay tdng quat ve ham sd tuin hoan, cac tac gia vSn gidi thieu dinh nghia ham sd tuin hoan (cudi §1) nham nhdc nhd hge sinh chii y tfnh chat tuan hoan cua cac ham sd lugng giac 4) Yeu ciu ve giai cac phucmg trinh lugng giac d day dugc giam nhe ra't nhidu so vdi trudc day Dieu dd the hien d hai didm co ban : - Chi neu cac dang phuomg trinh dom gian, khdng ddi hdi phai cd nhiing thu thuat bie'n ddi lugng giac phiic tap, va neu cd cac didu kien kem theo thi viec thir lai cac dieu kien dd kha dem gian - Khdng yeu ciu giai va bien luan phucmg trinh lugng giac chiia tham sd Tuy nhien, giao vien can chu y ren luyen cho hoc sinh kT nang giai cac phucmg trinh lugng giac ccr ban that thao Dd la ccf sd dd hoc sinh nang cao kT nang giai cac phuomg trinh phiic tap hom P h a n 2> CAC B A I SOAI^ §1 Cac ham so' Itfctog giac (tiet 1, 2, 3) I MUCTIEU Kie'n thurc HS nam dugc : Nhd lai bang gia tri lugng giac Ham sd y = sinx, ham sd y = cosx; su bidn thien, tfnh tuan hoan va cac tfnh chat cua hai ham sd Ham sd y = tanx, ham sd y = cotx; su bidn thien, tfnh tuin hoan va cac tfnh cha^t cua hai ham sd Tim hieu tfnh chit iuin hoan cua cac ham sd lugng giac Dd thi cua cac ham sd lugng giac KT nang ' • Sau hge xong bai nay, HS phai didn ta dugc tinh tuan hoan, chu ki tuin hoan va su bidn thien ciia cac ham sd lugng giac Bieu didn dugc dd thi cua cac ham sd lugng giac Mdi quan he giiia cac ham sd y = sinx va y = cosx Md'i quan he giiia cac ham sd y = tanx va y = cotx Thai Tu giac, tfch cue hge tap Biet phan biet rd cac khai niem eg ban va van dung tiing trudng hgp cu the Tu cac van de cua toan hge mgt each Idgic va he thdng Cdu hoi 12 Neu cdng thiic nghiem eua phuomg trinh cosx = cosa Cdu hoi 13 Neu cdng thiic nghiem cua phuong trinh tanx = tana Cdu hoi 14 Neu tdm tat each giai phuong trinh bac nhdt, bac hai ddi vdi mdt ham sd lugng giac Cdu hoi 15 Neu tdm tdt each giai phuomg trinh bac nhdt ddi vdi mdt sinx va cosx Cdu hoi 16 Neu didu kien cua a, b va e dd phucmg trinh asinx + bcosx = c cd nghiem HOAT DONG HLfdNG DAN B AI TAP SGK Bdi 43 Muc dich On tap lai su bidn thien cua cac ham sd lugng giac GV cho hge sinh tra ldi va kdt luan a) Diing; b)Sai; c) Diing; e) Sai; f) Dung; g) Sai d) Sai; Bdi 44 Muc dich On tap lai tfnh tudn hoan tua cac ham sdlugng giac Hoqt ddng cda GV Cdu hoi Hoqt dpng cda HS Ggi y tra Idi cSu hdi * Chiing minh Dat m = 2k, ham sd y = sinx tudn sin7i(x + m) = sin7ix hoan vdi chu ki 2n nen vdi mgi x, ta cd f(x + m) = sin[n(x + 2^)] = sin(;Dc + 2kn) = sin;zx =fix) 103 Hoqt dpng cua GV Hoqt dpng cda HS Cdu hoi Ggi y tra Idi c&u hdi Hay lap bang bidn thien cua GV cho HS tu lap bang bidn thien cua ham sd ham sd' Cdu hoi Ggi y tra Idi eSu hdi Ve dd thi cua ham sd GV treo dd thi chudn bi.san d nha va cho HSl.vdnha velai Bdi 45 Muc dich On tap lai dang asinx + bcosx = c Hoqt dpng cda HS Hoqt ddng cda GV Ggi y tra Idi c§u hdi Cdu hoi Dua bidu thiic Tt sinx +tan—COSX 71 smx + tan— cosx I f 71 71 smx COS— + COS XSin— Tti, 7 COS— ^ f 71 Tl-sm x + — vd dang Csin(x + a) COS — Ggi y tra Idi cau hdi Cdu hoi Dua bieu thiic Tt ;, tan— sinx + cosx ve dang Csin(x + a) 104 f 571 sin x + — cos-Tt I 14 Bdi 46 Muc dich On tap lai dang phuong trinh lugmg giac da hge Hoqt dpng cda HS Hoqt dpng cda GV Ggi y tra Idi cau hdi Cdu hoi Giai phuong trinh: 2TI^ sm X fti Ta cd eos2x = sin — 2x , dd: U = eos2x f Tt =sin — x J l2 sm X 7Tt , 2Tt , ' » x = — +k— vax = 18 Ggi y tra Idi cau hdi Cdu hoi Giai phuomg trinh: J 2Tt 7TI \-k2n tan(2x + ° ) t a n | l ° - =1 tan(2x + ° ) t a n [ l ° - - = ^ < m < l + V2 117 ... m6n toan ldp 10 , chiing toi tiep tuc bien scan bo sach: Thiet ke bai giang mon Toan ldp 11 Bg sach gom, cuon: Thiet kebdi gidng Hinh hoc 11 : 2 tap Thiei kebdi gidng Dgi sdvd Gidi tich 11 : 2 tap Thiit... kebdi gidng Dgi sdvd Gidi tich 11 : 2 tap Thiit kebdi gidng Hinh hoc 11 ndng cao: tap Thiit kebdi gidng Dgi sdvd Gidi tich 11 ndng cao: tap Day la b6 sach co nhieu hudng thiet ke, co nhieu dang, nhieu... hinh 1. 6 de neu dd thi cua ham sd tren • GV neu nhan xet SGK : 1) Khi X thay ddi, ham sd y = sinx nhan mgi gia tri thudc doan [ -1; 1] Ta ndi tap gid tri ciia ham sd y = sinx la doan [ -1; 1] 2)