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高中数学必修四三角恒等变换常考题型换

三角恒等变换常考题型分析 一选择题 1.在△ ABC 中,若 sin A ? sin B ? cos A cos B ,则△ ABC 一定为( A.等边三角形 B.直角三角形 C.锐角三角形 ).

D.钝角三角形 ). D.1

2. 3 tan 11? ? 3 tan 19? ? tan 11? ? tan 19? 的值是( A. 3 B.
3 3

C.0 ).
1 32

3. sin 6 ? ? cos 24 ? ? sin 78 ? ? cos 48 ? 的值为( A.
1 16

B. ?

1 16

C.

D.

1 8

4.已知 ? 为第二象限角, 25sin 2 ? ? sin ? ? 24 ? 0 ,则 cos A. ?
3 5

?
2

的值为( D. ?
4 5

).

B. ?

3 5

C.

2 2

x x x 6 5.已知不等式 f ? x ? ? 3 2 sin cos ? 6 cos 2 ? ? m ? 0 对于任意的 4 4 4 2
? 5? ? ? x ? 恒成立,则实数 m 的取值范围是( 6 6

). D. ? 3 ? m ? 3

A. m ? 3 二、填空题

B. m ? 3

C. m ? ? 3

3 3? ? 12 ? , ?) , sin(? ? ? ) ? ? , sin( ? ? ) ? ,则 cos(? ? ) ? 4 4 13 4 5 1 1 7.已知 sin ? ? sin ? ? , cos ? ? cos ? ? ,则 tan(? ? ? ) 的为 4 3

6.已知 ? , ? ? (

. . .

8.化简 sin( x ? 60?) ? 2 sin( x ? 60?) ? 3 cos(120? ? x) 的结果是 三、解答题 13.已知 cos(? ? 值.

?

1 ? 2 ? ) ? ? ,sin( ? ? ) ? ,0 ? ? ? ? ,0 ? ? ? ,求 cos(? ? ? ) 的 2 2 9 2 3

1

? sin(? ? ) 15 4 14.(1)已知 ? 为第二象限角,且 sin ? ? ,求 的值. sin 2? ? cos 2? ? 1 4
(2)已知 sin ? ? 2 cos? ? 0 ,求
cos 2? ? sin 2? 的值. 1 ? cos 2 ?

? 17.已知函数 f ( x ) ? sin( ? ? x )sin( ? x ) ? cos 2 x . 2

(1)求函数 f ( x) 的最小正周期; 区间.

? 3? (2)当 x ? [ ? , ] 时,求函数 f ( x) 的单调 8 8

18.如图,在平面直角坐标系 xOy 中,以 Ox 轴为始边作两个锐角 ? , ? ,它们的 终边分别与单位圆相交于 A , B 两点,已知 A , B 的横坐标分 别为
2 2 5 , . 10 5

(1)求 tan(? ? ? ) 的值;

(2)求 ? ? 2 ? 的值.

2


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