十年高考真题分类汇?2010-2019) 数学 专题05 三角函数 - 百度文库 ر

f(x)=cos(3x+6)=0,3x+6=2+k,kZ,x=9+3=

47

,,.3999ЦЦЦk

(3k+1)

,kZ.[0,]9

.

67.(2018ȫ1T16)֪f(x)=2sin x+sin 2x,f(x)Сֵ . 𰸡

33 2ɵT=2f(x)=2sin x+sin 2xһ,f(x)Сֵɿf(x)[0,2)ϵֵ.

f(x)=2sin x+sin 2x,f'(x)=2cos x+2cos 2x=4cosx+2cos x-2. f'(x)=0,ɵcos x=2cos x=-1,x[0,2)ʱ,x=3x=3x=. Ϊf(x)=2sin x+sin 2xֵֻx=

33533,f=-,f()=0,f(0)=0,Ժ()232

31

5

2

,x=

53,x=лx=0ʱȡ,f()=

3

f(x)СֵΪ-2.

3368.(2018աT7)֪y=sin(2x+)-2<<2ͼֱx=3Գ,յֵΪ_______. 𰸡?6 ɵsin(3+)=1,3+=2+k(kZ),=-6+k(kZ). Ϊ-<<,k=0,=-.

69.(2017T9)ƽֱϵxOy,ǦǦ¾OxΪʼ,ǵձ߹yԳ.sin =3,sin = 𰸡3 ɽǦǦµձ߹yԳ,æ+=2k+,kZ,=2k+-,kZ,sin

11

22ЦЦ

226=sin(2k+-)=sin =3.

70.(2017ȫ1T15)֪(0,),tan =2,cos(-)=__________.

24𰸡10

tan =2,sin =2cos . sin+cos=1,cos=5.

Ϊ(0,2),cos =5,sin =5.

21

52

2

2

1

Ц

3101

25Ϊcos(??-)=cos cos+sin sin, 444cos(??-4)=52+52=10.

71.(2017T12)ƽֱϵxOy,ǦǦ¾OxΪʼ,ǵձ߹yԳ.sin =3,cos(-)=________________. 𰸡-9 ɽǦǦµձ߹yԳƿɵæ=(2k+1)-,kZ,cos(-)=cos[2-(2k+1)]=-cos 2=2sin-1=2()-1=-.

3972.(2017աT5)tan(-)=,tan =________.

46𰸡 Ϊ

tan(??-)

475

1

2

ЦЦ

С522523101

7

12

7

=

1+tan??tan4tan??-tan4

=

tan??-11+tan??

2

=,tan =.

3

1675

73.(2017ȫ2T14)f(x)=sinx+3cos x-4(x[0,2])ֵ________. 𰸡1

֪f(x)=1-cos

2

313x+3cos x-4=-cos2x+3cos x+4=-(cos??-2)2

+1.

Ϊx[0,2],cos x[0,1]. Եcos x=ʱ,f(x)ȡֵ1.

2374.(2017ȫ2T13)f(x)=2cos x+sin xֵΪ . 𰸡5 Ϊf(x)=2cos x+sin x=5sin(x+)(tan =2),f(x)ֵΪ5. 75.(2016ȫ1T14)֪ǵ޽,sin(+4)=5,tan(-4)= . 𰸡- sin(??+4)=5,

3

43

3

cos(??-4)=cos[(??+4)-2]=5.

֦ǵ޽,-4ǵ޽.

ЦЦ3

sin(??-4)=-5.tan(??-4)=-3.

44

22

76.(2016ĴT11)sin 750= . 𰸡2 sin 750=sin(720+30)=sin 30=. 77.(2016ĴT11)cos8-sin8=_________. 𰸡2

cos8-sin8=cos4=2.

78.(2016㽭T10)֪2cosx+sin 2x=Asin(x+)+b(A>0),A=2,b= . 𰸡1

Ϊ2cosx+sin 2x=1+cos 2x+sin 2x=2sin(2??+)+1,A=2,b=1.

42

2

2

2

2

2

1

122С2

79.(2016ȫ3T14)y=sin x-3cos xͼɺy=sin x+3cos xͼƽ_______λȵõ. 𰸡 Ϊy=sin x+3cos x=2sin(??+),

3

23y=sin x-3cos x=2sinx-3=2sin[x-3+3],Ժy=sin x-3cos xͼɺy=sin x+3cos xͼƽ3λȵõ.

80.(2015աT8)֪tan =-2,tan(+)=,tan µֵΪ . 𰸡3

+2tan(??+??)-tan??

tan =tan[(+)-]=1+tan??tan(??+??)=72=3.

1-71

2

1781.(2015ĴT12)sin 15+sin 75ֵ_____________. 𰸡2

sin 15+sin 75=sin(45-30)+sin(45+30)

6=sin 45cos 30-cos 45sin 30+sin 45cos 30+cos 45sin 30=2sin 45cos 30=22

32=2. 22

682.(2015ĴT13)֪sin +2cos =0,2sin cos -cosֵ . 𰸡-1

sin +2cos =0,tan =-2.

23

2sin??cos??-cos2??

ԭʽ=sin2??+cos2??=

2tan??-1

tan2??+1=2(-2)-1(-2)+1

2=

-5

=-1. 583.(2015T14)֪f(x)=sin x+cos x(>0),xR.f(x)(-,)ڵ,Һy=f(x)ͼֱx=ضԳ,صֵΪ . 𰸡2 f(x)=sin x+cos x=2sin x+4,

Ϊf(x)(-,)ڵ,Һͼֱx=ضԳ,

f()Ϊһϵֵ,Цء+=2k+,kZ,Ԧ=+2k,kZ. ֦-(-)

2??̦Ц

422

42,ء,Ԧ=.

22

2̦84.(2015ϡT15)֪>0,ںy=2sin xy=2cos xͼĽ,̵ľΪ23,=____________. 𰸡 ͼʾ,ͬһֱϵ,y=2sin xy=2cos xͼ,A,BΪ.

2

A(

3

,2),B(-,-2), 4??4??

22

|AB|=23,á(??)+(22)=23, =2,=.

85.(2014ȫ2T14)f(x)=sin(x+2)-2sin cos(x+)ֵΪ . 𰸡1

f(x)=sin(x+2)-2sin cos(x+)

??2=sin[(x+)+]-2sin cos(x+)

24