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1 . 某公园计划改造一块四边形区域ABCD铺设草坪,其中
百米,
百米,
,
,草坪内需要规划4条人行道DM、DN、EM、EN以及两条排水沟AC、BD,其中M、N、E分别为边BC、AB、AC的中点.
,求排水沟BD的长;
(2)若
,试用
表示4条人行道的总长度.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7aeb2a8d1437eeb4482c3b6ad9f315.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd95dc30c0344788b94289c464a3158e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdb2dd10731b99c0f4f89ee957f8a239.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72c4340dcffb0783d118a587e5352a2d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/597ce705d3a2fe04d29de9e81ec6250d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
您最近一年使用:0次
名校
2 . 某公园计划改造一块四边形区域
铺设草坪,其中
百米,
百米,
,草坪内需要规划4条人行道
以及两条排水沟
、
,其中
分别为边
的中点.
,求
的余弦值;
(2)若
,求排水沟
的长;
(3)若
,试用
表示4条人行道的总长度.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7aeb2a8d1437eeb4482c3b6ad9f315.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0904a16358aab37c4042f40386d9d2d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2804e5b8e43f5c4622b96cc6dba646a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/214ba5ccd88a4f80292b4db8f81ade28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7db164a3e15489a0de6ac0203e2cba7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72c4340dcffb0783d118a587e5352a2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/727ad3e630a224303d6d3b8ad5c114ba.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72c4340dcffb0783d118a587e5352a2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/597ce705d3a2fe04d29de9e81ec6250d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
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3 . 在平面直角坐标系
中,利用公式
①(其中
,
,
,
为常数),将点
变换为点
的坐标,我们称该变换为线性变换,也称①为坐标变换公式,该变换公式①可由
,
,
,
组成的正方形数表
唯一确定,我们将
称为二阶矩阵,矩阵通常用大写英文字母
,
,…表示.
中,将点
绕原点
按逆时针旋转
得到点
(到原点距离不变),求点
的坐标;
(2)如图,在平面直角坐标系
中,将点
绕原点
按逆时针旋转
角得到点
(到原点距离不变),求坐标变换公式及对应的二阶矩阵;
(3)向量
(称为行向量形式),也可以写成
,这种形式的向量称为列向量,线性变换坐标公式①可以表示为:
,则称
是二阶矩阵
与向量
的乘积,设
是一个二阶矩阵,
,
是平面上的任意两个向量,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba6e18ee381b4e43352acb377fdb4bf0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44ee82573986d4fa6a7ee1b5f397edae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0859290725efef72a1b04f473d07da6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c84c4a85e9f31e35bc48c15d9873a03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c84c4a85e9f31e35bc48c15d9873a03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39822cb6df5463c27ac9bfed261a2ff6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d88591679796c52024d11c4de641bdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/762bfc20a2da28b3c59225851ea40036.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/762bfc20a2da28b3c59225851ea40036.png)
(2)如图,在平面直角坐标系
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44ee82573986d4fa6a7ee1b5f397edae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0859290725efef72a1b04f473d07da6e.png)
(3)向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4224bf1cbcd51f4cbdce93d981d65c5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c17f1f4912527319e32f60e7523c65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c26b9e508047e76f3a7ad88d587702ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cd47bfcd685d2466ee27c01bf286406.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c84c4a85e9f31e35bc48c15d9873a03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c17f1f4912527319e32f60e7523c65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f7a1df960feef63dec4790d63f52279.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1b8a88a16125366536cb4ad658e0cf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/595e7e1d74355ac82dcfc16b3e86cf78.png)
您最近一年使用:0次
2024-04-12更新
|
1946次组卷
|
7卷引用:安徽省皖江名校联盟2024届高三下学期4月模拟数学试题
安徽省皖江名校联盟2024届高三下学期4月模拟数学试题(已下线)模块五 专题5 全真拔高模拟1(高一人教B版期中)(已下线)数学(新高考卷02,新题型结构)(已下线)模块五 专题5 全真拔高模拟1(苏教版期中研习高一)(已下线)压轴题02圆锥曲线压轴题17题型汇总-1湖南省湘楚名校2023-2024学年高二下学期5月月考数学试题黑龙江省实验中学2024届高三第四次模拟考试数学试题
名校
4 . 在数学中,双曲函数是与三角函数类似的函数,最基本的双曲函数是双曲正弦函数与双曲余弦函数,其中双曲正弦函数:
,双曲余弦函数:
.(e是自然对数的底数,
).双曲函数的定义域是实数集,其自变量的值叫做双曲角,双曲函数出现于某些重要的线性微分方程的解中,譬如说定义悬链线和拉普拉斯方程.
(1)计算
的值;
(2)类比两角和的余弦公式,写出两角和的双曲余弦公式:
______,并加以证明;
(3)若对任意
,关于
的方程
有解,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3321510a9eb73909a36c084a8630e89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0099b9b80ed478824fa95677ebe9d5b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11204e2fb6e560bf7a4ca26eaebfc526.png)
(1)计算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e694af0c9f990ecb8b54b1c08bcc578e.png)
(2)类比两角和的余弦公式,写出两角和的双曲余弦公式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d92c32edc0e000405b7a6b9c48549959.png)
(3)若对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f78f05631a2ecb8bc3d379ca6c81f93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0edf67ed1367df200483579a294b5f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
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解题方法
5 . 通常用
分别表示
的三个内角
所对边的边长,
表示
的外接圆半径.
为圆心的
中,
和
是
的弦,其中
,
,求弦
的长;
(2)在
中,若
是钝角,求证:
;
(3)给定三个正实数
,其中
.问:
满足怎样的关系时,以
为边长,
为外接圆半径的
不存在、存在一个或存在两个(全等的三角形算作同一个)?在
存在的情况下,用
表示
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d2e072c68527ae3d3fc15b95cdb3edb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4020513c097ba34df4b42e297f892cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(2)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/194741f4d2ae7ee44cafca780361446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd0be39076f8a9425300e88e60ee9052.png)
(3)给定三个正实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0aadb354aceba145fa22173f87a00488.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2c659396f6a0f72e213185b1ab2e198.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0aadb354aceba145fa22173f87a00488.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0aadb354aceba145fa22173f87a00488.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
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解题方法
6 . 在平面直角坐标系中,锐角
、
的终边分别与单位圆交于
、
两点.
点的纵坐标为
,
点的横坐标为
,求
的值;
(2)若角
的终边与单位圆交于
点,经点
、
、
分别作
轴垂线,垂足分别为
、
、
.求证:线段
、
、
能构成一个三角形;
(3)探究第(2)小题中的三角形的外接圆面积是否为定值?若是,求出该定值,若不是,请说明理由.
![](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/5963abe8f421bd99a2aaa94831a951e9.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/954795d1842974a705f9468f3b952ab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eac97e6740365c85ad857aff85cefbe5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2aa6e4b697b41182cf163a0fb7e771a3.png)
(2)若角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15f5e8af5c6cfbecb2cdfbfb60dcdb1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b66a5b7813e902306477f91f9f4084cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/279563c3c055777ce1aa369a2ef54aed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
(3)探究第(2)小题中的三角形的外接圆面积是否为定值?若是,求出该定值,若不是,请说明理由.
您最近一年使用:0次
2023-04-13更新
|
483次组卷
|
2卷引用:陕西省西安市铁一中学2022-2023学年高一下学期期中数学试题
名校
解题方法
7 . 在平面直角坐标系中,锐角
的终边分别与单位圆交于A、B两点.
,B点的横坐标为
,求
的值;
(2)若角
的终与单位圆交于C点,设角
的正弦线分别为MA、NB、PC,求证:线段MA、NB、PC能构成一个三角形;
(3)探究第(2)小题中的三角形的外接圆面积是否为定值?若是,求出该定值,若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc14778010a33f90902ff17b1ec0ac73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/954795d1842974a705f9468f3b952ab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eac97e6740365c85ad857aff85cefbe5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2aa6e4b697b41182cf163a0fb7e771a3.png)
(2)若角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15f5e8af5c6cfbecb2cdfbfb60dcdb1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc04da053616157b39498a8a9868c875.png)
(3)探究第(2)小题中的三角形的外接圆面积是否为定值?若是,求出该定值,若不是,请说明理由.
您最近一年使用:0次
名校
解题方法
8 . 如图,在平面直角坐标系中.锐角
的终边分别与单位圆交于
两点,角
的终边与单位圆交于
点,过点
分别作
轴的垂线,垂足分别为
、
、
.
,
,求
的值;
(2)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4e288596fa3811dd2c17bded60e82e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52586ca2a3b783bc8092415e2d4bf6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8dc4c63a548b91061528aa11058de75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38335830b93ac4d99c28a8e209eecb3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c6efeb7234307a1ed17ec46b9a33242.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/018bb7f777002fd6efa1018fe0431b4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22d521f8d021b20757d7a68107fcef1d.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16a8789f95e66d48ef82d5a42808f525.png)
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名校
解题方法
9 . 燕山公园计划改造一块四边形区域
铺设草坪,其中
百米,
百米,
,
,草坪内需要规划
条人行道
、
、
、
以及两条排水沟
、
,其中
、
、
分别为边
、
、
的中点.
,求
的余弦值;
(2)若
,求排水沟
的长;
(3)当
变化时,求
条人行道总长度的最大值.(单位百米)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7aeb2a8d1437eeb4482c3b6ad9f315.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd95dc30c0344788b94289c464a3158e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdb2dd10731b99c0f4f89ee957f8a239.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a424b50eaeafa6f302ffd95476cb86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3533837e3d08c461dea031a44e5424d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b46c607b3deac746c0ef3389ad8f65c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c4c865445dda4a59b6d5cb18fd74404.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5abd5357df10d6bbfb60b284b42fd7d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/727ad3e630a224303d6d3b8ad5c114ba.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72c4340dcffb0783d118a587e5352a2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39b8d91afc34e4a9b0fdbb6bafb9087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
您最近一年使用:0次
2023-01-02更新
|
750次组卷
|
6卷引用:上海市奉贤中学2021-2022学年高一下学期5月月考数学试题
上海市奉贤中学2021-2022学年高一下学期5月月考数学试题(已下线)第12讲 余弦定理、正弦定理的应用(已下线)江西省上饶市2023届高三第一次高考模拟考试数学(理)试题变式题16-20第6章 三角(B卷·能力提升练)-【单元测试】2022-2023学年高一数学分层训练AB卷(沪教版2020必修第二册)(已下线)6.3 解三角形-高一数学同步精品课堂(沪教版2020必修第二册)(已下线)专题06 期末解答压轴题-《期末真题分类汇编》(上海专用)
解题方法
10 . 借助复数、三角及向量的知识,可以研究平面上点及图像的旋转问题.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O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;
(3)设
为不重合的两个定点,将点
绕点
按逆时针旋转
角得到点
,判断点
是否能够落在直线
上,若能,试用
表示相应
的值,若不能,说明理由.
(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/25f114df5ceabdb7e5fd3fdad4eaf056.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bc69e8d3fd54bb07d183a5ce38234e5.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)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870707dd29b0411bd3c348d662529df9.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/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8e7adca5c1f19c6fc21664a2a928ee9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
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