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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名校
2 . 已知角
的终边经过点
,角
为第三象限角,且__________.
求下列各式的值.在以下三个条件任选一个,补充在上面的横线上,并完成解答.
①
;②
;③
与
角终边关于
对称,
(1)
;
(2)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0f9f734c03d04c21edefa08e0acc1fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
求下列各式的值.在以下三个条件任选一个,补充在上面的横线上,并完成解答.
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a98b9c7ed16837433d01d05056806fc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71a91cc6022cd086e4740291459fd388.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31df243cbfc7408b105a0e12f7661423.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd2bc192468026593f5c6b4da761191.png)
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解题方法
3 . (1)计算![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2da73d3addae2a495783d8aeecf94acb.png)
(2)已知角
的终边过点
,求角
的三个三角函数值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2da73d3addae2a495783d8aeecf94acb.png)
(2)已知角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/135d867eac30e5a4cff409f70464a3fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
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4 . 设A是单位圆与x轴正半轴的交点,点B在单位圆上,且其横坐标为
,直角坐标系原点为O.
(1)设α是以OA为始边,OB为终边的角,求
的值;
(2)若P在单位圆上,且位于第一象限,点
在第二象限,求
的面积S的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af6ddf31b7d9225a4239883af72d153b.png)
(1)设α是以OA为始边,OB为终边的角,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cc9750c313ee972124cb62c4a6fb7ea.png)
(2)若P在单位圆上,且位于第一象限,点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af2cc5f8cec8c498aa12c99c04e1c97d.png)
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2021高一上·江苏·专题练习
5 . 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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