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广西陆川县中学高二上学期数学同步作业:第7章 直线与圆的方程 直线的倾斜角和斜率1(大纲版)

直线的倾斜角和斜率(1)
一、选择题 1.下列说法中正确的是 A.若直线的倾斜角为 ? ,则其斜率为 tan ? B.若直线的斜率为 tan ? ,则其倾斜角为 ? C.平行于 y 轴的直线,其倾斜角为 90 ? D.倾斜角为 90 ? 的直线必平行于 y 轴 2.已知 ? 是直线的倾斜角,那么 sin( A. [?1, ( )

?

4

? ? ) 的值属于的区间是
C. ( ?1,

2 ] 2

B. [?

2 2 , ] 2 2

2 ) 2

D. ( ?

2 2 , ] 2 2

3.直线的倾斜角的余弦为 A.

4 5

B. ?

4 5

3 ,则直线的斜率为 5 4 4 C. ? D. 3 3
2

4.一条直线的倾斜角的正弦满足方程 4x ? 4 3x ? 3 ? 0 ,则此直线的斜率为 A. 3 二、填空题 5.若直线 l 向上的方向与 y 轴正方向夹 30 ? ,则 l 的斜率为 。 B. ? 3

C.

3 3

D. ? 3 或 3

?1 6.函数 y ? f ( x) 与其反函数 y ? f ( x) 的对称轴 l1 绕原点按逆时针旋转 90 ? 得直线 l2 , 则直

线 l1 到直线 l2 的斜率 k 的变化范围是 7.若直线的斜率 k ? ( ? 3,



3 ) ,则该直线的倾斜角 ? 的取值范围是 3



8.如图所示,直线 l1, l2 , l3 的斜率分别为 k1, k2 , k3 ,则 k1, k2 , k3 的大小关系是 三、解答题 9.设直线 l 的斜率为 k ,求在下列情形中 l 的倾斜角: (1) | k |?



y

l2 l3
O

1 ? ; (2) k ? ? cot ? , ? ? (? ,0) 2 2

l1

x

10.已知直线的倾斜角为 ? ,且 cot ? ? k (k ? 0) ,求 ? ? f (k ) 的表达式。

11.已知直线 l 的倾斜角为 ? ,且 sin ? ? cos ? ?

1 ,求直线 l 的斜率。 5

参考答案 一、选择题 1.C 2.A 3.D 二、填空题 5. ? 3

4.D 7. [0,

2? ,? ) 8. k2 ? k3 ? k1 6 3 1 1 1 1 9.(1)若 k ? ,则倾斜角 ? ? arctan ;若 k ? ? ,则倾斜角 ? ? ? ? arctan 2 2 2 2
6. [1, ??) ? (??, ?1]

?

)?(

(2)倾斜角为 ? ? 10. ? ?

?

1 ? arctan k (或 ? ? ? ? arctan ) 2 k 4 11. kl ? ? 3

?

2


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