名校
解题方法
1 . 在
中,角
,
,
所对的边分别为
,
,
,已知
,
,其中
为
的面积.
(1)求角
的大小;
(2)设
是边
的中点,若
,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.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/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/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0658b38807dee29bef6899e2d428c03a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(1)求角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
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2卷引用:江苏省南京市东山高级中学南站校区2023-2024学年高一下学期期末考试数学试卷
解题方法
2 . 已知
分别为锐角三角形
三个内角
的对边,且
.
(1)求
;
(2)若
,
为
的中点,求中线
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05c976d105c27de505f83e7e40da698b.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d3ac959ebcb005ec9ebaff52f4ac70b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
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3卷引用:专题05 解三角形大题常考题型归类-期期末考点大串讲(人教B版2019必修第四册)
(已下线)专题05 解三角形大题常考题型归类-期期末考点大串讲(人教B版2019必修第四册)云南省大理市2023-2024学年高一下学期6月质量检测数学试题湖北省新高考联考协作体2023-2024学年高一下学期5月联考数学试题
名校
3 . 对任意两个非零向量
,
,定义:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2880d03a4fe19b30857292e07a7bb29d.png)
(1)若向量
,
,求
的值;
(2)若单位向量
,
满足
,求向量
与
的夹角的余弦值;
(3)若非零向量
,
满足
,向量
与
的夹角是锐角,且
是整数,求
的取值范围.
![](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/2880d03a4fe19b30857292e07a7bb29d.png)
(1)若向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dba6c7eb6216014862640716991326a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22249dd883332a917ec68eaf7dd5ea23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2eb893d1367e26f4388ae4280f78630.png)
(2)若单位向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcb0319e46d3d669c9439537e600c461.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bca35e52b8430246a1cf96e9e617cce.png)
(3)若非零向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaaa5755983415a0dd11a44c4f426efa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/189301a0467dfa2daf6b5806d15bfa22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09dd1004f81418675f8cfac07219d59c.png)
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|
4卷引用:吉林省部分名校2023-2024学年高一下学期联合考试数学试题
吉林省部分名校2023-2024学年高一下学期联合考试数学试题(已下线)专题03 平面向量的数量积常考题型归类-期末考点大串讲(人教B版2019必修第三册)重庆市璧山来凤中学等九校联考2023-2024学年高一下学期5月月考数学试题(已下线)【高一模块三】类型1 新定义新情境类型专练
名校
解题方法
4 . 平面向量是数学中一个非常重要的概念,它具有广泛的工具性,平面向量的引入与运用,大大拓展了数学分析和几何学的领域,使得许多问题的求解和理解更加简单和直观,在实际应用中,平面向量在工程、物理学、计算机图形等各个领域都有广泛的应用,平面向量可以方便地描述几何问题,进行代数运算,描述几何变换,表述物体的运动和速度等,因此熟练掌握平面向量的性质与运用,对于提高数学和物理学的理解和能力,具有非常重要的意义,平面向量
的大小可以由模来刻画,其方向可以由以
轴的非负半轴为始边,
所在射线为终边的角
来刻画.设
,则
.另外,将向量
绕点
按逆时针方向旋转
角后得到向量
.如果将
的坐标写成
(其中
,那么
.根据以上材料,回答下面问题:
,求向量
的坐标;
(2)用向量法证明余弦定理;
(3)如图,点
和
分别为等腰直角
和等腰直角
的直角顶点,连接DE,求DE的中点坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91174b2336306191ba275a87864172b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91174b2336306191ba275a87864172b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4293abac93e7633dc4c0fef321347e72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8a3b1b11c77ceb7ece55f76d2cd4618.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/873c064546108a5bce78bb71bc1e4a1e.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/ea99a712a0891faf366d4fec4dde5869.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abcb5d89b04570ceda2c29e11cb27a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/941b0d76d7b3108df49af338c989dc4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e32257bac4199820ccae5e7bd8377cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0849dbfc3775627925de0fe2e89c1692.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb50427d2e8a7c605bbd18ea8e0c3b79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af5f1b06a56fc382feed28e01f1ad102.png)
(2)用向量法证明余弦定理;
(3)如图,点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cd99c5000629d7f49499d666e68f40d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852b303689c31189cd47bb4a3220f9fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac451db3443cabb204f96c31fd4a02e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbfa1a2af7e38d33634c462300df381f.png)
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|
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|
3卷引用:高一下学期期末模拟卷(范围:必修第二册全册)-同步题型分类归纳讲与练(人教A版2019必修第二册)
(已下线)高一下学期期末模拟卷(范围:必修第二册全册)-同步题型分类归纳讲与练(人教A版2019必修第二册)湖南省永州市部分学校2023-2024学年高一下学期6月质量检测卷数学试题安徽省芜湖市第一中学2023-2024学年高一下学期期中考试数学试卷
名校
5 . 在
中,
,
是
的外心,
.
(1)求边
的长;
(2)若
为
的中点,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56aadf1458daecb860ea53e8fbe031b3.png)
(1)求边
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbc0f23e79770ac886bf6c4f5937d0dc.png)
您最近一年使用:0次
解题方法
6 . 已知向量
,向量
与向量
的夹角为
.
(1)求
的值.
(2)若
,求实数
的值.
(3)在(2)的条件下,求向量
在向量
方向上的投影向量的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf6d915a3019f08498f59037b342f421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aefd06c239145a2b6ae87a955aa51414.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8addbfcc46330524fdc9fd4f1532ab5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(3)在(2)的条件下,求向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73a0b19e69be46452425916a0fcb49c9.png)
您最近一年使用:0次
名校
解题方法
7 . 如图,
的内角
的对边分别为
,已知
,
为线段
上一点,且
.
;
(2)若
,求
面积的最大值;
(3)若
,求
.
![](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/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89889ba8a8175b5c4ceec37465193418.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff400c098ae6bf6abd24651a5a21114e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d783fe7f3ce673d5d21281174e7a7968.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5321ef782f50670b895f93bf08b61b98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4600275dda575e545cab0145d9480d.png)
您最近一年使用:0次
2024高一下·全国·专题练习
8 . 已知复数
,
,
.
(1)若
为实数,求
的值;
(2)设复数
在复平面内对应的向量分别是
,若
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee2e5eabc6f1a836db026ab78e4fd71c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ed0e6475b373adeee38a6892fb78d05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42947a9ec7c9d436aad88d7ee568445a.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fe615164ed2995bdeea0f5b0ba94231.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
(2)设复数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90d860cb86e1467ac24010aecfc7a425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b172cf8d898883d82e973f28c3c3a3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98a76970598da2e8562f99251b100ee1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b986f54ac055bbe5ea946087182a4d98.png)
您最近一年使用:0次
名校
9 . 已知在任意一个三角形的三条边上分别向外做出三个等边三角形,则这三个等边三角形的中心也构成一个等边三角形;我们称由这三个等边三角形中心构成的三角形为其外拿破仑三角形.在锐角
中,角
所对的边分别为
且
,以
的边
分别向外作的三个等边三角形的中心分别记为
,且
的面积为
,记
为
的外接圆半径.
,求
;
(2)若
,求
面积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38335830b93ac4d99c28a8e209eecb3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9f054a8f158340bc788136124632325.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39900a2d790732077ffb571427a134fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b372e638a9dbed3bbf92454d816d212.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2a5a1f585c19f582edbb8cf73c58c6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4310db23fc79936c7182361e652bab1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.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/1c0f2a532c86e3f4a1cd508839363b05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d46be1fb12ca82fdef75149d22bc1c94.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8843442efe0889ebbd393484ff8596cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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解题方法
10 . 在
中角A,B,C的对边分别为a,b,c,且
.
(1)求角C的大小;
(2)若
,
,CH为AB边上的高,H为垂足,
,其中m,
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63e1e867d056ae92954e8c8fed547840.png)
(1)求角C的大小;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03837b3769eda7f0d3804cc5ad4a6d60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65397f11ea8af736f38debadf420c4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/225bfd80ba9c9d6d6a25c51fbd63c6be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8440725e1df5ca0990b572dd84127914.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0be44077d42cfffece905b1af13e000.png)
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