Tran Sú Tuứng kim tra ẹaùi soỏ 10 CHNG VI: CUNG V GểC LNG GIC KIM TRA 1 TIT S 1 Phn I: Trc nghim khỏch quan (3 im, mi cõu 0.5 im) Cõu 1: iu kin trong ng thc tan.cot = 1 l: a) k , k Z 2 + b) k , k Z 2 c) k , k Z d) k2 , k Z 2 + Cõu 2: Tớnh , bit cos = 0. a) k2 , k Z 2 = + b) k2 , k Z 2 = + c) k , k Z 2 = + d) k2 , k Z = Cõu 3: Cho P = sin( + ) cos( ) v Q sin cos 2 2 = + ữ ữ . a) P + Q = 0 b) P + Q = 1 c) P + Q = 2 d) P + Q = 1 Cõu 4: Cho k , k Z 2 + . Ta luụn cú: a) 1 tan 1 b) tan 0 c) tan x R / x k , k Z 2 + d) tan R Cõu 5: sin3xcos5x sin5xcos3x = ? a) sin8x b) sin2x c) sin2x d) cos8x Cõu 6: n gin biu thc sina sin3a sin5a P cosa cos3a cos5a + + = + + . Chn li gii ỳng trong cỏc li gii: a) sina sin3a sin5a sin9a sin P tan cosa cos3a cos5a cos9a cos + + = = = = + + b) sina sin3a sin5a sin9a P tan9a cosa cos3a cos5a cos9a + + = = = + + c) sina sin3a sin5a P tana tan3a tan 5a tan 9a cosa cos3a cos5a + + = = + + = + + d) 2sin3acos2a sin3a sin3a(2cos2a 1) sin3a P tan3a 2 cos3a cos2a cos3a cos3a(2cos2a 1) cos3a + + = = = = + + 1 kim tra ẹaùi soỏ 10 Tran Sú Tuứng Phn II: T lun (7 im) Cõu 1: (3 im) 3 2 3 Cho sina a , cos b b 5 2 3 2 = < < = < < ữ ữ . Tớnh cos(a + b). Cõu 2: (2 im) Bin i thnh tớch s biu thc A = cos 2 a cos 2 3a. Cõu 3: (2 im) Chng minh rng trong tam giỏc ABC, ta cú: sin2A + sin2B + sin2C = 4sinAsinBsinC ================= 2 Tran Sú Tuứng kim tra ẹaùi soỏ 10 CHNG VI: CUNG V GểC LNG GIC KIM TRA 1 TIT S 2 I. PHN TRC NGHIM KHCH QUAN ( 4 im) Cõu 1. Trờn ng trũn lung giỏc, cho im M vi AM = 1 nh hỡnh v di õy : Hóy chn cõu ỳng : a) sAM = 1 k2+ , k Z b) sAM = 1 k2 + , k Z c) sAM = 3 k2 + , k Z d) sAM = 11 6 k2 + , k Z Cõu 2. Bit sinx = 1 5 v 2 x < < . Giỏ tr ca cosx l : a) 4 5 b) 24 25 c) 2 6 5 d) 4 5 Cõu 3. Bit 4 2 < < , hóy chn cõu ỳng : a) cot 0 < b) tan2 0 < c) cos3 0 > d) sin 4 0 > Cõu 4. Hóy chn ng thc ỳng vi mi a : a) cos2a = 1 2cos2a b) sina = 2 sin a 2 .cos a 2 c) sin4a = 4 sina . cosa d) sin2a = 1 2 sina . cosa II. PHN T LUN ( 6 im) Cõu 1. Cho A = sin( 4 + ) + sin( 4 ) (2 im) a. Chng minh rng : A = 2 .sin , R (1 im) b. Tỡm 2 ( ; ) A = 2 2 . ( 1 im) Cõu 2. Bit tan 2 a 2 3 = , tớnh cosa v sin2a . ( 2 im) Cõu 3. Tớnh giỏ tr ca biu thc A = ( cos110 0 + cos10 0 ) 2 cos 2 50 0 . ( 2 im) ================= 3 AA / B / B O M x / x y / y kim tra ẹaùi soỏ 10 Tran Sú Tuứng CHNG VI: CUNG V GểC LNG GIC KIM TRA 1 TIT S 3 Phn I: Trc nghim khỏch quan (3) Cõu 1: (0,5) cho gúc x tho món 90 0 <x<180 0 . Mnh no sau õy l ỳng? a) sinx < 0 b) cosx <0 c)tgx >0 d) cotgx>0 Cõu 2: (0,5) i 25 0 ra radian. Gn bng bao nhiờu? a) 0,44 b) 1433,1 c) 22,608 rad Cõu 3: (0,5) Tớnh giỏ tr biu thc : P = cos23 0 + cos215 0 + cos275 0 + cos287 0 a) P = 0 b) P = 1 c) P = 2 d) P = 4 Cõu 4: (1,5) ỏnh du x thớch hp vo ụ trng: S TT Cung Trờn ng trũn lng giỏc im cui ca cung trựng vi im cui ca cung cú s o ỳng Sai 1 = 552 0 12 0 2 = 1125 0 45 0 3 = 35 2 2 Phn II: T lun (7) Cõu 1: (3) Rỳt gn biu thc sau: A = 2 2 sin(a b)sin(a b) cos a.cos b + Cõu 2: (4 ) Chng minh cỏc ng thc sau: a) 2 2 1 sin2x tgx 1 tgx 1 sin x cos x + + = b) 1 cosx sin x sin x 1 cosx = + (vi x k ,k Z) =========================== 4 Tran Sú Tuứng kim tra ẹaùi soỏ 10 CHNG VI: CUNG V GểC LNG GIC KIM TRA 1 TIT S 4 I. PHN TRC NGHIM (3im): Cõu 1. Trong cỏc h thc sau, h thc no ỳng: a) 1 + tan 2 a = 2 1 sin a (sina 0) b) sin4a = 4 sinacosa c) sin 2 2a + cos 2 2a = 1 d) 1 + cot 2 a = 2 1 cos a (cosa 0). Cõu 2. Cho sina = 1 3 , vi 90 0 < a < 180 0 . Giỏ tr ca cosa l: a) 2 2 3 b) 8 9 c) 2 2 3 d) 2 3 Cõu 3. Cho tam giỏc ABC, tan(3A + B + C).cot(B + C A) cú giỏ tr bng: a) 2 b) 1 c) 4 d) 1 Cõu 4. Cho 0 < a, b < 2 v 1 1 tga ,tgb . 2 3 = = Gúc a+ b cú giỏ tr bng : a) 3 4 b) 1 c) 4 d) 5 4 Cõu 5. Cho tga = 2. Giỏ tr biu thc sin2a + 2cos2a bng: a) 6 5 b) 5 6 c) 6 5 d) 5 6 Cõu 6. Giỏ tr biu thc : A= sin 2 0 2 0 2 0 1 45 cot g 60 cos 135 + bng a) 7 6 b) 6 7 c) 7 6 d) 6 7 II. PHN T LUN (7 im) Cõu 1. Cho cosa = 3 5 vi a 4 2 < < . Tớnh cos2a, sin2a. Cõu 2. Chng minh cỏc ng thc a) 3 3 1 cos asin a sin a cos a sin 4a 4 = b) 2 2 sỡn2a sin a sin a 8 8 2 + = ữ ữ Cõu 3. Chng minh rng tam giỏc ABC cõn nu sin B 2 cos A sin C = . Cõu 4. Chng minh biu thc khụng ph thuc x, y: A= 2 2 2 2 2 2 sin x tg y cos x sin x tg y cos y + =================== 5 . 2cos2a bng: a) 6 5 b) 5 6 c) 6 5 d) 5 6 Cõu 6. Giỏ tr biu thc : A= sin 2 0 2 0 2 0 1 45 cot g 60 cos 13 5 + bng a) 7 6 b) 6 7 c) 7 6 d) 6 7 II. PHN T. sin3a(2cos2a 1) sin3a P tan3a 2 cos3a cos2a cos3a cos3a(2cos2a 1) cos3a + + = = = = + + 1 kim tra ẹaùi soỏ 10 Tran Sú Tuứng Phn II: T lun (7 im) Cõu 1: (3 im)