1 . 在二维直角坐标系中,一个位置向量的旋转公式可以由三角函数的几何意义推出.如:将向量
绕坐标原点
逆时针方向旋转
得到向量
,由
,以
为终边的角为
,则点
,进而求得点
.借助复数、三角及向量的知识,可以研究平面上点及图象的旋转问题.请尝试解答下列问题:
(1)在直角坐标系中,已知点
的坐标为
,将
绕坐标原点
逆时针方向旋转
至
.求点
的坐标;
(2)设向量
,把向量
按顺时针方向旋转
角得到向量
,求向量
对应的复数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b7d9f40ce4648c9729f49cc071fe631.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31dd289f71c1c828803e8a2831b99e83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb3240777c7a7e633f93dffb25a9f6f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4f605ec0729ce6d72237ad662a06862.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11d2905505abc9014422a5cf590f9d94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/898bbbb917649895f6113368bec5de70.png)
(1)在直角坐标系中,已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80991c1f0c963104740e50cfff6f29a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15615de1a6df206dbd081251f676578e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
(2)设向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/873c064546108a5bce78bb71bc1e4a1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abcb5d89b04570ceda2c29e11cb27a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af5f1b06a56fc382feed28e01f1ad102.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af5f1b06a56fc382feed28e01f1ad102.png)
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2 . 在平面直角坐标系xOy中,点P从点
出发,在以原点O为圆心,2为半径的圆上按逆时针方向做匀速圆周运动,且每秒钟转动3弧度,记t秒时点P的纵坐标为
.
(1)求
的解析式;
(2)若点P的纵坐标第n次等于
的时刻记为
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fb8c1ac253f504497962194df593bb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2709ca478fb15ea08e8aa55328eae8e6.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2709ca478fb15ea08e8aa55328eae8e6.png)
(2)若点P的纵坐标第n次等于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9297e289a9ef977009186083ec738ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8af36bffeb6c6b916b59884063fc73b1.png)
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2021高一上·江苏·专题练习
3 . 设函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6230be733604a67c0594ebeb10d14890.png)
(1)若角
的顶点与原点
重合,始边与
轴的非负半轴重合,它的终边过点
,求
的值;
(2)若
,函数
是奇函数,求
的值;
(3)若
,是否存在实数
,使得函数
的最小值为
,如果存在,求出实数
的值;如果不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6230be733604a67c0594ebeb10d14890.png)
(1)若角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a9d86d46657a5e186e6a8ed698474c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47d7f440c63f1cc2199857b0c6e74ee6.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f687593cb4ecef31667bf2320fdfe000.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/800412cade2e256b1f313603b28587df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ce485410257c9c1fae9d87ce3e44cc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9987521a298dc846d8bf70d84e96a661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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