名校
解题方法
1 . 如图一:球面上的任意两个与球心不在同一条直线上的点和球心确定一个平面,该平面与球相交的图形称为球的大圆,任意两点都可以用大圆上的劣弧进行连接.过球面一点的两个大圆弧,分别在弧所在的两个半圆内作公共直径的垂线,两条垂线的夹角称为这两个弧的夹角.如图二:现给出球面上三个点,其任意两个不与球心共线,将它们两两用大圆上的劣弧连起来的封闭图形称为球面三角形.两点间的弧长定义为球面三角形的边长,两个弧的夹角定义为球面三角形的角.现设图二球面三角形
的三边长为
,
,
,三个角大小为
,
,
,球的半径为
.![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf538440bd45e5881f2b22994560ba7a.png)
(2)①求球面三角形
的面积
(用
,
,
,
表示).
②证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.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/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f435efcc7869eec21bdba1ed81dc3f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf538440bd45e5881f2b22994560ba7a.png)
(2)①求球面三角形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.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/9f435efcc7869eec21bdba1ed81dc3f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
②证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f314e3f1d6311f0476623d4e55484a3e.png)
您最近一年使用:0次
2023-04-21更新
|
384次组卷
|
4卷引用:浙江省A9协作体2022-2023学年高一下学期期中联考数学试题
浙江省A9协作体2022-2023学年高一下学期期中联考数学试题江苏省徐州市第一中学2022-2023学年高一下学期期中数学试题(已下线)13.3 空间图形的表面积和体积(分层练习)(已下线)11.1.5 旋转体-【帮课堂】(人教B版2019必修第四册)
名校
解题方法
2 . 对于定义域为R的函数
,如果存在常数T,
,使得
是以T为周期的函数,则称函数
为正弦周期函数,且称常数T为
的正弦周期.
已知函数
满足以下四个条件:
①函数
是以T为正弦周期的正弦周期函数;
②函数
的值域为R;
③函数
在区间
上单调递增:
④
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294bab9bbfb414f2d1fb0844aee4fc9e.png)
(1)分别判断函数
、
是否为正弦周期函数.如果是正弦周期函数,写出它的正弦周期,(不需证明).
(2)设
,求证:对任意
,存在唯一的
使得
.
(3)求证:对于任意的
,都有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7eecacbdc5c2a7e7ac00daea8c448098.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16a0ab6eeb2b475795eae6f432789105.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93e03ad0c315806342d6cd732a0b91a3.png)
①函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93e03ad0c315806342d6cd732a0b91a3.png)
②函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93e03ad0c315806342d6cd732a0b91a3.png)
③函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93e03ad0c315806342d6cd732a0b91a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaafa094244d569dd54bd8036c7f0b6d.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93941e7f4bea588b5020035760ba0e05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294bab9bbfb414f2d1fb0844aee4fc9e.png)
(1)分别判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f19e893159870d911d83af4f4b2b70ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6978ab291c9908f871c1178a2dea35a9.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a46e678bf9d2df5ad4c782b3dc22f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/761e8a1b81490a2db7aa84f2104cb3fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea34ffa60956e957a07faf386e43a20c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0b836129720c860faf76f2703b61016.png)
(3)求证:对于任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f7999305fcdf5fd209920cc42cfe6f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aab11dce5b8ee5cbe5f1439c1b9e4dc3.png)
您最近一年使用:0次
名校
解题方法
3 . 如图(1),正三棱柱
,将其上底面ABC绕
的中心逆时针旋转
,
,分别连接
得到如图(2)的八面体
,依次连接该八面体侧棱
的中点分别为M,N,P,Q,R,S,
(ⅰ)求证:
共面;
(ⅱ)求多边形
的面积;
(2)求该八面体体积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a3a008a5ce2f3e0d93bf1b31f1e941d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1b73c7e51c2fbe79faa78e5287d2ccc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ff5cc57686ee7429fee0907651083c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78a40d2cf43fce0c99dff3470d554eb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ff5cc57686ee7429fee0907651083c4.png)
(ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8ae231960760617a585b8478185d8ac.png)
(ⅱ)求多边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac3662c929bd88085eb96dd4797482de.png)
(2)求该八面体体积的最大值.
您最近一年使用:0次
名校
解题方法
4 . 已知
,其中
.
(1)当
,
时,
①任意写出
的一条对称轴;
②求证:
;
(2)若对任意
,
,求
所能取到的最小值和最大值,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aba354888ba7e2065e85656c20f31005.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/360ff131c51a4ef6745538c18cec92c2.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/191d9381c4f252fbb5553ba72462d0aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5805d32dc3582d0a706c015875c15eb9.png)
①任意写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
②求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
(2)若对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d6fc9b90f370fbb27552876b650f8f.png)
您最近一年使用:0次
解题方法
5 . 三角形的布洛卡点是法国数学家、数学教育学家克洛尔于1816年首次发现,但他的发现并未被当时的人们所注意.1875年,布洛卡点被一个数学爱好者布洛卡重新发现,并用他的名字命名.当
内一点
满足条件
时,则称点
为
的布洛卡点,角
为布洛卡角.如图,在
中,角
所对边长分别为
,点
为
的布洛卡点,其布洛卡角为
.
.求证:
①
(
为
的面积);
②
为等边三角形.
(2)若
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec15e5cb6d4dc2cf6ba0bedd87514448.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.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/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d7b9d9bf0d5fc25c99170ab27fa4045.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa010342528037783c29e6fc705d5bba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5cbff84327e964f912a54032e76ccc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6492fa033f83d0775b049476612b86ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e02df6f963e47a894cce8b4ad469ec.png)
您最近一年使用:0次
2024-04-24更新
|
629次组卷
|
3卷引用:江苏省常州市教育学会2023-2024学年高一下学期4月学业水平监测数学试题
名校
解题方法
6 . 在
中,角
,
,
的对边分别为
,
,
,点
,
,
分别位于
,
,
所在直线上,满足
,
,
(
,
,
).
是边长为3的正三角形,且
,求
;
(2)如图2,若
,
,
交于一点
,
①求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/454845e47d30210e1052f288c04a3828.png)
②若
,
,
,
,求
.
![](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/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9abaeba15f3abdd877bc701af52c5cd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05edc2270435e31e1c6246f2e73d319c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c730e8a8b00a42f640f47bdbe0ced2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8b8c1e566d5c3d13d732e99b5214da8.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/d1a609b7b505947a8a2f34fbed4b2208.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6d7ff5d48857835f5127cb41cd607bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dc8047ecbb77a3c5f61ab430b2279f3.png)
(2)如图2,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
①求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/454845e47d30210e1052f288c04a3828.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ea1abafdbaa3ed5568822c52ee19af5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25ef5a4055fb0bac59cc504a71735417.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52dde258c86bc5af02e2eee95448d0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fab7aa572678c1776345bcb4d622393.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5cbff84327e964f912a54032e76ccc9.png)
您最近一年使用:0次
2024-04-23更新
|
745次组卷
|
4卷引用:模块五 专题五 全真拔高模拟(高一)
(已下线)模块五 专题五 全真拔高模拟(高一)(已下线)模块五 专题5 全真拔高模拟1(北师版高一期中)福建省厦门第一中学2023-2024学年高一下学期第一次适应性训练(月考)数学试题福建省厦门第一中学2023-2024学年高一下学期第一次适应性数学试题
7 . 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)
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2024-04-12更新
|
1944次组卷
|
7卷引用:模块五 专题5 全真拔高模拟1(高一人教B版期中)
(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)模块五 专题5 全真拔高模拟1(苏教版期中研习高一)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)数学(新高考卷02,新题型结构)(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
解题方法
8 . 如图1,等腰
满足
,
,
于
.如图2,将
绕着直线SA旋转时,在BA旋转而成的平面
内总有点
满足
,
,(点
,点
分别在直线BD两侧).
长;
(2)求证:
平面
;
(3)记三棱锥
的体积为
,三棱锥
的体积为
,当四棱锥
的体积最大时,求
值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79482c6de6bbd05affc78f9c625e52f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2affc8264f2e40743bb12dd7ea57177b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fe85217cea14241255ec21200b25b16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fe0bb7d51e559e73aa16a954fe7fa33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79482c6de6bbd05affc78f9c625e52f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abd284f76d9f5769bc189508ce2572b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c279c8033acb94c3f91be2e05b0a6bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/833cfda415649b832cc136caed392753.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a6e2867f32d3f1c3cd36cd3a11a8580.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10c83f8945042b9c8fb2fbdac9308d62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(3)记三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d535bfd65eb04a29d64425d54b2acf86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4764374bd2fb78e59cd0b283637baeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69dd9f16a5c7a66e62e52fd66f4449ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63055a5d6916f99d07fede49120753f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c773ac7c3a6575fb7d432c93fe5f2a32.png)
您最近一年使用:0次
名校
解题方法
9 . 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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昨日更新
|
310次组卷
|
3卷引用: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
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(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
名校
10 . 对于平面向量
,定义“
变换”:
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8560ca9023cf64637ce1467f338556bd.png)
(1)若向量
,
,求
;
(2)已知
,
,且
与
不平行,
,
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d128ae3e21294e2eac5bcc775ccfb03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a18fd5445fb8a04b925a2745a56f613.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fddd9dc1110e60973b7b9e43bb1f9d15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8560ca9023cf64637ce1467f338556bd.png)
(1)若向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ea462b0382581d99c8bba51d9b79f09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3e186ebc624ebacde9a03b96289f1ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2e900404ba71110c5861ced9634646f.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22601439d36b6a93453d738c2b803eb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc499d2e731df31957eeaa355bfbac4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4f605ec0729ce6d72237ad662a06862.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fc9656d8286c4d6fa309d6ae347c89e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a63cf7e5f25165ccf0e24d32add179ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a176f300a2462e4f1ffef99d30c21e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39e719e667f2783febbec38dea080b98.png)
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