73055e.cc:人教版高中数学必修四3.2简单的三角恒等变换(三)练习【学生版】.docx

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高中数学学习材料
鼎尚图文*整理制作

简单的三角恒等变换(三)

一、选择题

1、已知 tan? ? ? 4 ,则 tan(? ? 1 ? ) 的值是 ( )

3

4

A.-7

B. ? 1 7

C.7

2.已知 cos(? ? x) ? 3 , x ? (? ,2? ) ,则 sin x ? ( ) 5

A. ? 3 5

B. ? 4 5

C. 3 D. 4

5

5

3、函数 y ? sin2 x ? sin x cos x 的最小正周期 T= ( )

D. 1 7

A.2π

B.π

C. ? 2

D. ? 3

4.函数 y ? 2 cos2 (x ? ? ) ?1的一个单调递增区间是 ( ) 4

A. (? , 3? ) 22

B. (? , 3? ) 44

C. (? ? , ? ) 22

D. (? ? , ? ) 44

5.已知 tan? ? 4 ,则 sin? ? cos? 的值为 ( ) 3 sin? ? cos?

A. 1 3

B. ? 1 3

C.7

D. ? 7

6.已知? 是第二象限角,且 sin? ? 3 ,则 tan 2? ? ( ) 5

A. 24 7

B. ? 24 7

C. 7 24

D. ? 7 24

二、填空题

7、把函数 y ? sin 2x 的图象向左平移 ? 个单位长度,再把所得图象上所有点的横坐标伸长到原来的 2 倍(纵 4

坐标不变),所得函数图象的解析式为



8、若角? 的始边为 x 轴非负半轴,顶点是原点,点 P(?4,3) 为其终边上一点,则 cos 2? 的值为



9、已知

f

(x)

?

c os 3x 2

cos x 2

?

sin

3x 2

sin

x 2

?

2 s in

x cosx

,当

x

?

?? ?? 2

,?

? ??



f

(x)

的零点为

.

10、已知函数 f (x) ? Asin(?x ??), (A ? 0,? ? 0, ? ? ? , x ? R) 的图象的一部分如下图所示,则函数 f (x) 2

的解析式为

.

三、解答题

11、已知函数 f (x) ? 2sin x cos x ? 2 cos2 x ?1 ,

(1)求 f (x) 的最大值及相应的 x 的值;

(2)若

f

(? )

?

3 5

,求

cos

2

? ??

π 4

?

2?

? ??

的值。


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