《三角恒等变换》基础测试题(已排版,可直接打印)(学生卷)

必修 4 第三章《三角恒等变换》基础训练题
一.选择题 (每小题5分,共 50 分) 1. 方程 2 cos x ? 1 的解集为( ) A. {x | x ? 2k? ?

?

3

, k ? Z}

B. {x | x ? 2k? ? 5? , k ? Z }
3

C. {x | x ? 2k? ?

?
3

, k ? Z}

D. {x | x ? k? ? (?1) k

?
3

, k ? Z}

2 ,则 sin A ? cos A ? ( ) 3 5 5 15 15 A. B. ? C. D. ? 3 3 3 3 sin x ? cos x tan x ? cot x sin x ?cos x tan x ?cot x ? ? ? ? 3. 函数 f ( x) ? 在 x ? (o, ) 时的最小值为( ) sin x ? tan x cos x ? tan x cos x ? cot x sin x ? cot x 2
2. 若△ ABC 的内角 A 满足 sin 2 A ? A.2 B.4 C.6 ) D. D.8 4. 函数 f ( x) ? sin 2 x ? sin 4 x 的最小正周期是( A .2π 5. 已知 ? ? ( B.π C.

3 ? , ? ),sin ? ? , 则 tan(? ? ) 等于( ) 2 5 4 1 1 A. B. 7 C. ? D. ?7 7 7 2 6. A 为三角形的一个内角,且 sin A ? cos A ? ,则 sin 2 A 与 cos 2 A 的值依次为( 2
A.

?

? 2

? 4

)

1 3 , 2 2
4 ? 3

B. ?

1 3 , 2 2
2 ? 3

C. ?

1 3 ,? 2 2

D.

1 3 ,? 2 2
)

7. 设 0 ? ? ? ? ? ? ? 2?且 sin ? ? sin ? ? sin ? ? 0 , cos? ? cos ? ? cos? ? 0 ,则 ? ? ? 等于( A. B.

3 ,则 sin 2x 的值为( ) 4 5 19 16 14 A. B. C. 25 25 25 9. 设锐角 ? 满足 tan(? ? ? ) ? 3 ? 2 2 ,则 cos ? 值是( 4
8. 已知 sin(

?

2 4 ?或 ? 3 3

C.

D.都不对

? x) ?

D. )

7 25

A.

2 2

B.

3 2

C.

3 3

D.

6 3
)

10. 已知 cos( ? ? ? ) ? A.7

3 ? ? , ? ? ( , ? ), 则 tan( ? ? ) 的值为( 5 2 4 1 1 B.7 C. ? D. 7 7

二.填空题 (每小题 5 分,共 25 分) 11. 已知 sin2α +sin2β +sin2r=1(α 、β 、r 均为锐角),则 cosα cosβ cosr 的最大值等于_____. 12. 函数 y ? sin x ?

1 cos x( x ? R ) 的最大值为 2

.

4 4 13. 设 f ( x) ? sin x ? sin x cos x ? cos x ,则 f (x) 的值域是__________

1 ? ) ? , 那么tan(? ? )的值是________. 4 4 4 1 ? 3? 15. 已知 sin ? ? cos ? ? ,且 ≤ ? ≤ ,则 cos 2? 的值是__________ 5 2 4
14. 如果tan(? ? ? ) ? , tan(? ?

2 5

?


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