名校
1 . 如图,在平面直角坐标系
中,半径为1的圆
沿着
轴正向无滑动地滚动,点
为圆
上一个定点,其初始位置为原点
为
绕点
转过的角度(单位:弧度,
).
表示点
的横坐标
和纵坐标
;
(2)设点
的轨迹在点
处的切线存在,且倾斜角为
,求证:
为定值;
(3)若平面内一条光滑曲线
上每个点的坐标均可表示为
,则该光滑曲线长度为
,其中函数
满足
.当点
自点
滚动到点
时,其轨迹
为一条光滑曲线,求
的长度.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02c9643bf4dd7e04efa4644412491725.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c81b29ac8a01886b25dcef55c5f6877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2ce55c4ff508755d16c375625437027.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69218ef831edc8173b4029ea99eda87.png)
(3)若平面内一条光滑曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc031988b2a4dcd840069dbd3a1c810e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dfe48a76ae71f8925b731e8c330bdb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5d69e7fb25c60ee47440a1ece037544.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8a8bcf6ef69b6bdfc84e8472a259bf5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/016b58ad9076316abaf809dea297256a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/016b58ad9076316abaf809dea297256a.png)
您最近一年使用:0次
2024-03-13更新
|
1235次组卷
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3卷引用:河南省南阳市西峡县第一高级中学2023-2024学年高二下学期第一次月考数学试卷
名校
2 . 在
中,角A,B,C的对边分别为a,b,c.已知AB⊥AD,
,
=![](https://staticzujuan.xkw.com/quesimg/Upload/formula/535e95d241e9c978c10355dcb07da256.png)
.函数
.
(1)若
,求
的值域;
(2)若对于任何有意义的边a,
在
上有解,求b的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3677d5b65dcb496e8a8a6fdb6ad4f6be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5cbff84327e964f912a54032e76ccc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/535e95d241e9c978c10355dcb07da256.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60d4cbfc00ff1b4016bc51b6704f6c42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08dbc1a722e424a5d46233e4e7895a69.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/3/59f621ef-808f-45e1-b64b-df992a771e3e.png?resizew=141)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48adb8a59b5c02fad5eada1b35171cf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若对于任何有意义的边a,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba83e35d73fa41612e302b0a8a06ae6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0417ce6e34b21cf42fe0e572a43c207.png)
您最近一年使用:0次
2023-08-02更新
|
1331次组卷
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5卷引用:江西省宁冈中学2023-2024学年高二上学期开学考试数学试题
江西省宁冈中学2023-2024学年高二上学期开学考试数学试题辽宁省葫芦岛市2022-2023学年高一下学期期末数学试题(已下线)专题02 解三角形(2)-【常考压轴题】(已下线)专题04解三角形的7种常考题型归类-《期末真题分类汇编》(北师大版(2019))(已下线)专题09高一数学下学期期末考点大汇总-《期末真题分类汇编》(人教B版2019必修第四册)
名校
3 . 如图,已知
,
分别为
两边上的点,
,
,过点
,
作圆弧,
为
的中点,且
则线段
长度的最大值为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d7b2fe01a33c4825f9974ed9663a99c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56150248dd4b787a2013311e4737e93f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91f1c40ebcc993a5778478154c124f0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5a6b11637ea396e989ab32d780e745b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0284e9ec571566921b9071f678f28638.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84fb85c78522640bcaf889f89ad89de9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/14/a707c65d-04d1-4c0b-9f41-2e1f244c0da5.png?resizew=181)
您最近一年使用:0次
2023-02-09更新
|
1555次组卷
|
4卷引用:广东省深圳市龙岗区深圳科学高中2023-2024学年高二上学期第一次月考数学试题
名校
解题方法
4 . 正四棱锥
的展开图如图所示,侧棱
长为1,记
,其表面积记为
,体积记为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/e2bf084b-f7e5-47d8-add0-6ed4bfada543.png?resizew=202)
(1)求
的解析式,并直接写出
的取值范围;
(2)求
,并将其化简为
的形式,其中
为常数;
(3)试判断
是否存在最大值,最小值?(写出结论即可)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a6e2867f32d3f1c3cd36cd3a11a8580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3c55c1c441f921d874702a4f19ed17f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/794f2c6bd63355105d179d11306a9cae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c9d76fb48eb30e7946cb96047e08206.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/e2bf084b-f7e5-47d8-add0-6ed4bfada543.png?resizew=202)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/794f2c6bd63355105d179d11306a9cae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29d0adafeb8e5d088e974f1246880055.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a296bb758c36b50b102a4ceb2dea42bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
(3)试判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29d0adafeb8e5d088e974f1246880055.png)
您最近一年使用:0次
2022-07-05更新
|
815次组卷
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7卷引用:上海市洋泾中学2022-2023学年高二上学期期中数学试题
上海市洋泾中学2022-2023学年高二上学期期中数学试题湖北省郧阳中学、恩施高中、沙市中学、随州二中、襄阳三中2022-2023学年高二上学期10月联考数学试题湖北省五校(郧阳中学、恩施高中、沙市中学、随州二中、襄阳三中)2022-2023学年高二上学期10月月考数学试题湖北省黄石市第二中学2023-2024学年高二上学期9月月考数学试题(已下线)期中测试卷01(测试范围:第10-11章)-2023-2024学年高二数学单元速记·巧练(沪教版2020必修第三册)北京一零一中学2021-2022 学年高一下学期期末考试数学模拟试题(一)(已下线)湖南省长沙市雅礼中学2024届高三上学期月考(二)数学试题变式题19-22
5 . 周口市广播电视塔位于周口市区七一路和周口大道交叉口处,该塔有效地解决了周口市广播电视无线信号覆盖范围小、信号质量差的问题.发射塔由塔座、塔身、井道、塔楼和天线等
个主要部分组成(如图1所示),其中天线为传统的四边形空间桁架结构,横截面层层缩进,在外形上有着芝麻开花节节高的吉祥寓意.国庆假期,章阳同学在取得有关部门许可的前提下,利用无人机对广播电视塔进行拍照与摄像.章阳同学在地面点
处测得塔楼
的仰角为
,无人机在
处沿仰角为
的方向飞行
米后到达
处,测得
,且
,
,
,
,
五个点都在同一平面内(如图2所示).
![](https://img.xkw.com/dksih/QBM/2021/11/23/2857692062326784/2858053833318400/STEM/e903456d9f8a45e48f6930dc665e1ca6.png?resizew=554)
(1)求塔楼到地面的高度
;
(2)如果广播电视塔的天线
的长是
米,无人机从
到
的飞行过程中,在点
处观看天线
的视角为
(即
),为了拍摄到天线
最为清晰的图像,要求视角
最大.若点
处距离地面的高度
为
米,那么
为何值时,无人机拍摄到天线
的图像最清晰?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.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/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eaf15952853fb42e8fd9a726598f67ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f3ecac7aca747ed5e6ef84d907869e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f2665526efab6fdd59a4fe1bfe4e39.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/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://img.xkw.com/dksih/QBM/2021/11/23/2857692062326784/2858053833318400/STEM/e903456d9f8a45e48f6930dc665e1ca6.png?resizew=554)
(1)求塔楼到地面的高度
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
(2)如果广播电视塔的天线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b765e032d24c1557ff29cb6f70be0a98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26689ae5eba9a29775b20d7a2dcd3ace.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb26d84907c923278ac4626a9d58947.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
您最近一年使用:0次
2021-11-24更新
|
572次组卷
|
3卷引用:河南省九师联考2021-2022学年高二上学期期中考试文科数学试题
20-21高一下·上海浦东新·期末
名校
6 . 已知
,向量
,
,
、
、
是坐标平面上的三点,使得
,
.
(1)若
,
的坐标为
,求
;
(2)若
,
,求
的最大值;
(3)若存在
,使得当
时,△
为等边三角形,求
的所有可能值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce632c0ad85f24096c0f05d5450e473e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2aa1670a597db4dcc5e481c9eb41dc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27945773ec2b92d380eaddc5026836c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/797e67927616b141ed7c6b83f8b6f4fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a9066cefc9b9b13bec0a2b62540d1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16b2299483e9e9ce35f12538e10b4ff7.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a0f96c4dfd44a0412601f183a8c7443.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e3db90f04d3df749923b1763de1b58c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/312d5e0158617b367cb0fd246c83bb36.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0817e4c901a4729662505086e7ec6c69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6ea4ced7d3817604c02e8793f28ccf5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c31fbfce3b4faf00ab7e4388f37ecc5d.png)
(3)若存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b7cbba6f130b84315180391c177d0c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d92355504a42ddba1d0f03d5db455858.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56448a74c1b8430c425d79d626764f4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
您最近一年使用:0次
2021-07-12更新
|
1006次组卷
|
9卷引用:上海高二下学期期末真题精选(压轴60题35个考点专练)-【满分全攻略】2022-2023学年高二数学下学期核心考点+重难点讲练与测试(沪教版2020选修一+选修二)
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