ye1688:上海市上海中学2014-2015学年高一下学期数学练习(三)试卷

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2016 届高一数学练习三
一、填空题: 1、利用诱导公式化简: (1) sin( x ? ? ) ? (3) tan( (2) sec(?630? ? ? ) ? (4) cos( x ? ? ) ?
2 ? 2 ?

?
2

? x) ?
2 ?

2、求值: sin 1 ? sin 2 ? ? ? sin 89 ? 3、设 ? , ? ? [ ?

? ?
?

, ] ,且满足 sin ? cos ? ? cos ? sin ? ? 1 ,则 sin ? ? cos ? ? 2 2

4、已知 tan1234 ? a ,那么 sin(?206? ) ? sin(296? ) ? 5、已知角 ? , ? 的顶点在坐标原点,始边为 x 轴的正半轴重合, ? , ? ? (0, ? ) ,角 ? 的终边与单位 圆焦点的横坐标为 ? 6、化简 sin(

?

1 4 ,角 ? ? ? 的终边与单位圆交点的纵坐标是 ,则 cos? ? 3 5

? ? ) cos( ? ? ) ? sin( ? ? ) sin( ? ? ) ? 4 3 4 3

?

?

?

7、已知 ? , ? 满足 sin ? ? 2sin ? ? 1 ,那么 cos ? ? 2cos ? 的最大值是 8、 3sin ? ? sin(2? ? ? ) ,且 tan ? ? 2 ,那么 tan(? ? ? ) ?

a sin
9、已知正实数 a , b 满足

5 ? tan 8? ,那么 b ? ? ? a 15 a sin ? b cos 5 5 5

?

? b cos

?

二、填空题: 1、若 A 是第二象限角,那么 A.第一象限角 2、已知 cos( x ?

A ? 和 ? A 都不是 2 2
C.第三象限角 D.第四象限角

B.第二象限角

?
6

)??

? 3 ,则 cos x ? cos( x ? ) 的值是 3 3
2 3 3
C. ?1 D. ?1

A. ? 3、

2 3 3

B. ?

sin(2 x ? y ) ? 2 cos( x ? y ) 等于 sin x

A.

sin( x ? y ) sin x

B.

2 sin y sin x

C.

sin x sin y

D.

sin y sin x

4、已知 ? , ? 均为锐角, sin ? ? x, cos ? ? y, cos(? ? ? ) ? ?

3 4 3 1 ? x 2 ? x( ? x ? 1) 5 5 5 3 4 3 1 ? x 2 ? x(0 ? x ? ) C. y ? ? 5 5 5 n? , n ? Z }, M 5、 M ? {x | x ? ?2 cos 3
A. y ? ? A. M ? N B. M ? N

3 ,则 y 与 x 的函数关系式为 5 3 4 1 ? x 2 ? x(0 ? x ? 1) B. y ? ? 5 5 3 4 1 ? x 2 ? x(0 ? x ? 1) D. y ? ? 5 5 2n ? 3 ? {x | x ? ?2sin ? , n ? Z } ,则 M 与 N 的关系是 6
C. N ? M D. M ? N ? ?

6、在 ?ABC 中,若 sin A ? A.

16 65

B.

56 65

3 5 , cos B ? ,则 cos C 的值是 5 13 16 56 16 C. 或 D. ? 65 65 65

三、解答题 1、已知 sin ? 是方程 10 x ? x ? 3 ? 0 的根,且 ? 为第三象限角,
2

3 3 sin(? ? ? ) ? sin( ? ? ? ) tan 2 (2? ? ? ) tan(? ? ? ) 2 2 求 cos( ? ? ) cos( ? ? ) 2 2

?

?

2、 (1)若 cos(

?

4 3 ? x) ? ? , ? ? x ? ? ,求 sin x ? cos x ; 4 5 2
2

(2)化简 sin (? ?

?

) ? sin 2 (? ? ) ? sin 2 ? 。 6 6

?


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