1 . 若函数
的图象恒过
和
两点,则称函数
为“
函数”.
(1)判断下面两个函数是否是“
函数”,并说明理由:
①
;②
.
(2)若函数
是“
函数”,求
;
(3)设
,定义在
上的函数
满足:
①对
,均有
;
②
是“
函数”,求函数
的解析式及实数a的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b2c84e7b41a841a230ed5f8a42309aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29343388ca8b33dc98325e65382b38a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a359f9aeb5add5377519c6f7650ae6f.png)
(1)判断下面两个函数是否是“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a359f9aeb5add5377519c6f7650ae6f.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5e0f9a2c91af4b28879a32fb027fc7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d6ee41a3a8869cd2f4d9f230d008741.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e17afd02a58c3d3c25ac4f8cab171e24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a359f9aeb5add5377519c6f7650ae6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e93e7062f9483ecc0bc8f40916a7824a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
①对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d13ba6d93a671ca21730facc7fbf052c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ae03ea9aabc605c52dada45c5b0502f.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c50bb5280d82386a5496ff8f4434661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a359f9aeb5add5377519c6f7650ae6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
您最近一年使用:0次
名校
2 . 借助三角函数定义及向量知识,可以方便地讨论平面上点及图象的旋转问题.试解答下列问题.
(1)在直角坐标系中,点
,将点
绕坐标原点
按逆时针方向旋转
到点
,如果终边经过点
的角记为
,那么终边经过点
的角记为
.试用三角函数定义,求点
的坐标;
(2)如图,设向量
,把向量
按逆时针方向旋转
角得向量
,试用h、k、θ表示向量
的坐标;
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/12/c795a170-83f8-4bb9-a7f1-b86b0144183b.png?resizew=98)
(3)设
、
为不重合的两定点,将点B绕点A按逆时针方向旋转
角得点C.判断C是不能够落在直线
上,若能,请求出θ的三角函数值(正弦、余弦、正切不限),若不能,说明理由.
(1)在直角坐标系中,点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/675de67c4df38e172f7de40b03508fb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c67d01e61dc0042e67b5e8ec8e727c22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3982ebdedf29c3890e6e891263bfbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(2)如图,设向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/550d5fb27e50cbe46bc1586be89cab8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9795e7f5cb9b366776c41d8f3f43942.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be64d59ac6538a0f4d79fb825e082081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be64d59ac6538a0f4d79fb825e082081.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/12/c795a170-83f8-4bb9-a7f1-b86b0144183b.png?resizew=98)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bdb225f362f150791f7483a96a18d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72babdedbe6b32b150cc3ee258a7c310.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
您最近一年使用:0次
2021-07-24更新
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490次组卷
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6卷引用:北京市一六六中学2020-2021学年高一下学期期中考试数学试题
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