luong giac 11

cosin O cotang

sin

tangp A MQB T' aI. H THC C BN1. nh ngha cc gi tr lng gic:cossintan' cotOP aOQ aAT aBT aNhn xt: , 1 cos 1; 1sin 1 a a tana xc nh khi ,2a k k Z + , cota xc nh khi , a k k Z 2. Du ca cc gi tr lng gic:Trang 10CHNG 0CNG THC LNG GICCHNG 0CNG THC LNG GICTCung phn tGi tr lng gicI II II IVsina + + cosa + +tana + + cota + + 3. H thc c bn: sin2a + cos2a = 1;tana.cota = 12 22 21 11 tan ; 1 cotcos sina aa a+ + 4. Cung lin kt: Cung i nhau Cung b nhau Cung ph nhaucos( ) cos a a ( ) sin sin a a sin cos2a a| ` . ,sin( ) sin a a cos( ) cos a a cos sin2a a| ` . ,tan( ) tan a a tan( ) tan a a tan cot2a a| ` . ,cot( ) cot a a cot( ) cot a a cot tan2a a| ` . ,5. Bng gi tr lng gic ca cc gc (cung) c bitTrang 10Cung hn km Cung hn km 2sin( ) sin a a + sin cos2a a| `+ . ,cos( ) cos a a + cos sin2a a| `+ . ,tan( ) tan a a + tan cot2a a| `+ . ,cot( ) cot a a + cot tan2a a| `+ . ,II. CNG THC CNGCng thc cng: III. CNG THC NHN1. Cng thc nhn i: sin2a = 2sina.cosa2 2 2 2cos2 cos sin 2cos 1 1 2sin a a a a a

222tan cot 1tan2 ; cot22cot1 tana aa aaa 2. Cng thc h bc: 3. Cng thc nhn ba:Trang 1006432 23 343220030045060090012001350180027003600sin 0122232132220 1 0cos 1322212012221 0 1tan 03313 3 1 0 0sin( ) sin .cos sin .cos ab a b b a + +sin( ) sin .cos sin .cos ab a b b a cos( ) cos .cos sin .sin ab a b a b + cos( ) cos .cos sin .sin ab a b a b +tan tantan( )1 tan .tana baba b++ tan tantan( )1 tan .tana baba b +3332sin3 3sin 4sincos3 4cos 3cos3tan tantan31 3tana a aa a aa aaa 2221 cos2sin21 cos2cos21 cos2tan1 cos2aaaaaaa++4. Cng thc biu dinsina, cosa, tanatheo t = tan 2a: t: tan ( 2 )2at a k + th: 22sin1 tat+;221cos1 tat+; 22tan1 tatIV. CNG THC BIN I1. Cng thc bin i tng thnh tch:sin sin 2sin .cos2 2ab aba b+ + sin sin 2cos .sin2 2ab aba b+ cos cos 2cos .cos2 2ab aba b+ + cos cos 2sin .sin2 2ab aba b+ sin( )tan tancos .cosaba ba b++ sin( )tan tancos .cosaba ba b sin( )cot cotsin .sinaba ba b++ sin( )cot cotsin .baa basinb sin cos 2.sin 2.cos4 4a a a a| ` | `+ + . , . , sin cos 2sin 2cos4 4a a a a| ` | ` + . , . , 2. Cng thc bin i tch thnh tng:1cos .cos cos( ) cos( )21sin .sin cos( ) cos( )21sin .cos sin( ) sin( )2a b ab aba b ab aba b ab ab ] + + ] ] + ] ] + + ]Vn 1:TP XC NH, TP GI TR, TNH CHN L, CHU KTrang 10Chng I: HM S LNG GIC V PHNG TRNH LNG GICChng I: HM S LNG GIC V PHNG TRNH LNG GICI. HM S LNG GIC I. HM S LNG GIC sin y x : Tp xc nh D = R; tp gi tr 1, 1 T] ]; hm l, chu k 02 T .* y = sin(ax + b) c chu k 02Ta* y = sin(f(x)) xc nh ( ) f x xc nh.cos y x : Tp xc nh D = R; Tp gi tr 1, 1 T] ]; hm chn, chu k 02 T .* y = cos(ax + b) c chu k 02Ta* y = cos(f(x)) xc nh ( ) f x xc nh.tan y x : Tp xc nh\ ,2D R k k Z + ' ' ; tp gi tr T = R, hm l, chu k 0T .* y = tan(ax + b) c chu k 0Ta* y = tan(f(x)) xc nh ( ) f x ( )2k k Z + cot y x : Tp xc nh{ \ , D R k k Z ; tp gi tr T = R, hm l, chu k 0T .* y = cot(ax + b) c chu k 0Ta* y = cot(f(x)) xc nh ( ) ( ) f x k k Z .* y = f1(x) c chu k T1 ;y = f2(x) c chu k T2Trang 20Th hm s 1 2( ) ( ) y fx f x t c chu k T0 l bi chung nh nht ca T1 v T2.Bi 1Tm tp xc nh v tp gi tr ca cc hm s sau:a/ 2sin1xyx| ` . ,b/ sin y x c/ 2 sin y x d/ 21 cos y x e/ 1sin 1yx+f/ tan6y x| ` . ,g/ cot3y x| ` + . ,h/ sincos( )xyxi/y = 1tan 1 xBi 2Tm gi tr ln nht, gi tr nh nht ca hm s:a/y = 2sin 14x| `+ + . ,b/2 cos 1 3 y x + c/sin y x d/ 24sin 4sin 3 y x x +e/2cos 2sin 2 y x x + +f/ 4 2sin 2cos 1 y x x +g/y = sinx + cosx h/y =3sin2 cos2 x x i/y = sin 3cos 3 x x + +Bi 3 Xt tnh chn l ca hm s:a/y = sin2x b/y = 2sinx + 3 c/y = sinx + cosxd/y = tanx + cotx e/y = sin4x f/y = sinx.cosxg/y= sin tansin cotx xx x+h/y= 33cos 1sinxx+i/y = tan xBi 4Tm chu k ca hm s:a/ sin2 y x b/ cos3xy c/ 2sin y x d/ sin2 cos2xy x +e/ tan cot3 y x x +f/ 3 2cos sin5 7x xy g/ 2sin . cos3 y x x h/ 2cos 4 y x i/y = tan(3x + 1)Trang 30S: a/. b/ 6p. c/ . d/4p.e/ p. f/ 70p. g/ p. h/ .4 i/3Vn 2: TH CA HM S LNG GIC1/ V th hm s lng gic: Tm tp xc nh D. Tm chu k T0 ca hm s. Xc nh tnh chn l (nu cn). Lp bng bin thin trn mt on c di bng chu k T0 c th chn:00, x T] ] hoc 0 0,2 2T Tx ] ] ]. V th trn on c di bng chu k. Ri suy ra phn th cn li bng php tnh tin theo vc t 0. . v kT i r r v bn tri v phi song song vi trc honh Ox (vi ir l vc t n v trn trc Ox).2/ Mt s php bin i th:a/ T th hm s y = f(x), suy ra th hm s y = f(x) + a bng cch tnh tin th y = f(x) ln trn trc honh a n v nu a > 0 v tnh tin xung pha di trc honh a n v nu a < 0.b/ T th y = f(x), suy ra th y = f(x) bng cch ly i xng th y = f(x) qua trc honh.c/ th( ), neu f(x) 0( )-f(x), neu f(x)