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jx.ct10000.com:11专题十一 三角函数式的求值、化简、证明

2012 年高考复习资料—第二轮复习专题练习题 华中师大一附中 孟昭奎

专题十一
一、选择题

三角函数式的求值、化简、证明

1. (2008 年高考·浙江卷)若 cosα +2sinα =- 5 ,则 tanα =( A.

) D.-2 )

1 2

B.2

C.-

1 2

2. (2008 年高考·山东卷)已知 cos(α A.3.若

2 3 5

B.

2 3 5

π 4 7 )+sinα = 3 ,则 sin(α + π)的值是( 5 6 6 4 4 C.D. 5 5

cos2α 2 ,则 cosα +sinα 的值为( ) ?? π 2 sin(α ? ) 4 7 1 1 A.B.C. 2 2 2 2 2sin2α cos α ? 4.化简 =( ) 1 ? cos2α cos2α
A.tanα 5.在△ABC 中,已知 tan ①tanA·cotB=1 B.tan2α C.1

D.

7 2

D.

1 2

A?B =sinC,给出以下四个论断: 2
②0<sinA+sinB≤ 2

③sin2A+cos2B=1 ④cos2A+cos2B=sin2C 其中正确的是( ) A.①③ B.②④ C.①④ 6.△ABC 中,3sinA+4cosB=6, 4sinB+3cosA=1,则角 C 的大小为( A.

D.②③ ) D.

π 2π 或 3 3 π π α ?β 7.已知方程 x2+4ax+3a+1=0(a>1)的两根为 tanα 、tanβ ,且α , ∈(- , ),则 tan β 的 2 2 2
B.

π 6

5π 6

C.

π 5π 或 6 6

值是( A.



1 2

B.-2

C.

4 3

D.

1 或-2 2

二、填空题

3 ? sin 70? =________. 2 ? cos2 10? tan(α ? 1004?) ? tan(α ? 1004?) 9.已知 2005sin2α =sin2008°,则 的值为________. tan(α ? 1004?) ? tan(α ? 1004?)
8. (2008 年高考·宁夏/海南卷) 10. (2007 年高考·浙江卷)已知 sinθ +cosθ = _________.
专题十一 三角函数式的求值、化简、证明

1 π 3π ,且 ≤θ ≤ ,则 cos2θ 的值是 5 2 4

2012 年高考复习资料—第二轮复习专题练习题 华中师大一附中 孟昭奎

11.2002 年在北京召开的国际数学家大会,会标是以我国古代数 学家赵爽的弦图为基础设计的, 弦图是由四个全等直角三角形与一 个小正方形拼成的一个大正方形(如图) ,如果小正方形的面积为 1, 大正方形的面积为 25, 直角三角形中较小的锐角为θ , 那么 cos2 θ 的值等于_________. 三、解答题

π 1 ? 2sin(2x ? ) 4 . 12.已知函数 f(x) ? cosx
(1)求 f(x)的定义域; (2)设α 是第四象限的角,且 tanα =-

4 ,求 f( α )的值. 3

13. (2008 年高考·江西卷)在△ABC 中,a、b、c 分别为角 A、B、C 所对的边长,a= 2 3 , tan

A A?B C +tan =4, sinBsinC=cos2 2 .求 A、B 及 b、c. 2 2
3 ), n=(cosA, sinA),且 m·n=1.

14.已知 A、B、C 是△ABC 三内角,向量 m=(-1, (1)求角 A; (2)若

1 ? sin2B ? ?3 ,求 tanC. cos 2B ? sin 2B

15.已知△ABC 的面积为 3,且满足 0≤ AB · AC ≤6,设 AB 和 AC 的夹角为θ . (1)求θ 的取值范围; (2)求函数 f(θ )=2sin2(

π +θ )- 3 cos2θ 的最大值与最小值. 4

专题十一

三角函数式的求值、化简、证明


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