名校
1 . 某公园计划在矩形空地上建造一个扇形花园如图①所示,矩形
的
边与
边的长分别为48米与40米,扇形的圆心
为
中点,扇形的圆弧端点
,
分别在
与
上,圆弧的中点
在
上.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/4/42c484aa-8b21-48d3-823e-7ba4dfeb255a.png?resizew=375)
(1)求扇形花园的面积(精确到1平方米);
(2)若在扇形花园内开辟出一个矩形区域
为花卉展览区.如图②所示,矩形
的四条边与矩形
的对应边平行,点
,
分别在
,
上,点
,
在扇形的弧上.某同学猜想:当矩形
面积最大时,两矩形
与
的形状恰好相同(即长与宽之比相同),试求花卉展览区
面积的最大值,并判断上述猜想是否正确(请说明理由).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.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/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/4/42c484aa-8b21-48d3-823e-7ba4dfeb255a.png?resizew=375)
(1)求扇形花园的面积(精确到1平方米);
(2)若在扇形花园内开辟出一个矩形区域
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a299d2b999568e80be8005565ba209a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cad4595d5352b2884568a59d8d766a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6795cae2df43a722e1355e9562d93c09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
您最近一年使用:0次
2020-05-21更新
|
366次组卷
|
3卷引用:2020届上海市黄浦区高三二模(阶段性调研)数学试题
名校
解题方法
2 . 已知函数
,
的图像为曲线C,两端点为
,点
为线段AB上的一点,其中
,
,点P,Q均在曲线C上,且点P的横坐标等于
点Q的纵坐标为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b364f509e943a0d45284e82c6970e832.png)
(1)设![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bbf7495fe027d4251a9c78373d5e69c.png)
,求点P,Q的坐标;
(2)设
,求
的面积的最大值及相应
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e207cf62e3a7e282eac4c4a3455bbf9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61363caaf38d70abba2090a4546bf6a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3511cdc6a9b56bc1d9415d3d94ef0f67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7982aecdeab24efdc1e17d7a6aede43c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3be362dec96173f246ff747264007817.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c39d222f7eb9ba7c9bf47a2966dc890.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b364f509e943a0d45284e82c6970e832.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bbf7495fe027d4251a9c78373d5e69c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdfec4233214c3a729c843dee0d186db.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b5940708617cc6f6f62fd35508d712f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84a9dabb53dc826019fc8b6ae6d940c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
3 . 求下列方程的解集:
(1)
;
(2)
;
(3)
;
(4)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f05e208f2c6a9b81a3fb4787987b87f.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2587252e961c9ad810ec5e1a2cd00141.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ffc8001092c38d90963c404bd40f58d.png)
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb500e8652a0eb7ad7a1e345810d10d.png)
您最近一年使用:0次
名校
解题方法
4 . 如图,长方体
中,
,
,点
为面
的对角线
上的动点(不包括端点).
平面
交
于点
,
于点
.
![](https://img.xkw.com/dksih/QBM/2020/1/17/2379205671772160/2380930300198912/STEM/61e50b82f1674c6faf6b397987f5ea8f.png?resizew=125)
(1)设
,将
长表示为
的函数;
(2)当
最小时,求异面直线
与
所成角的大小.(结果用反三角函数值表示)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27db558e8db4c957654c8e5cecd2d2dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55a2310cbba5e050488cd9296eb195d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ebb05874eb3353d754af24c9974273e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83c09eec4e14a861af83d7828797d176.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a7442b64b37f685bc3ae88ff450c1a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dee50a23604ea2a9c1f3649dab97c2e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://img.xkw.com/dksih/QBM/2020/1/17/2379205671772160/2380930300198912/STEM/61e50b82f1674c6faf6b397987f5ea8f.png?resizew=125)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8711eddf26d11fc974dfb6da4b640918.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c8ffe24cf9f327aeb241225ab15ab1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c8ffe24cf9f327aeb241225ab15ab1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c8ffe24cf9f327aeb241225ab15ab1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
您最近一年使用:0次
2020-01-20更新
|
270次组卷
|
3卷引用:上海市金山中学2015-2016学年高二下学期第一次月考数学试题
5 . 某校兴趣小组在如图所示的矩形区域
内举行机器人拦截挑战赛,在
处按
方向释放机器人甲,同时在
处按某方向释放机器人乙,设机器人乙在
处成功拦截机器人甲.若点
在矩形区域
内(包含边界),则挑战成功,否则挑战失败.已知
米,
为
中点,机器人乙的速度是机器人甲的速度的
倍,比赛中两机器人均按匀速直线运动方式行进,记
与
的夹角为
.
(1)若
,
足够长,则如何设置机器人乙的释放角度才能挑战成功?
(2)如何设计矩形区域
的宽
的长度,才能确保无论
的值为多少,总可以通过设置机器人乙的释放角度使机器人乙在矩形区域
内成功拦截机器人甲?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95e62758f556745c4089a0b178c6f8b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d00be47dcb89793f14a2fd10f4c522b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95e62758f556745c4089a0b178c6f8b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d868a22c50b4ad3dae8e438c9779d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/4/70768327-a170-4df8-a2bc-9e025e71f719.png?resizew=166)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bc1f08c7640e62e8717abf4d44a6c83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
(2)如何设计矩形区域
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
6 . 如图,一智能扫地机器人在
处发现位于它正西方向的
处和北偏东
方向上的
处分别有需要清扫的垃圾,红外线感应测量发现机器人到
的距离比到
的距离少0.4米,于是选择沿
路线清扫,已知智能扫地机器人的直线行走速度为0.2米/秒,10秒钟完成了清扫任务(忽略机器人吸入垃圾及在
处旋转所用时间)
![](https://img.xkw.com/dksih/QBM/2020/8/20/2531991121051648/2541711547441152/STEM/3e2c6ef2e8bf441da6942ca434ecf76e.png?resizew=186)
(1)
、
两处垃圾的距离是多少?
(2)求智能扫地机器人此次清扫过程中旋转角的最小值?请指出旋转方向.
![](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/c67d01e61dc0042e67b5e8ec8e727c22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/bfd66776565f049eb453c14fcaf79234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://img.xkw.com/dksih/QBM/2020/8/20/2531991121051648/2541711547441152/STEM/3e2c6ef2e8bf441da6942ca434ecf76e.png?resizew=186)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)求智能扫地机器人此次清扫过程中旋转角的最小值?请指出旋转方向.
您最近一年使用:0次
2020-09-03更新
|
252次组卷
|
4卷引用:2020届上海市七宝中学高三高考押题卷数学试题
2020届上海市七宝中学高三高考押题卷数学试题(已下线)考点03 三角函数与解三角形-2021年高考数学【热点·重点·难点】专练(上海专用)(已下线)课时21 反三角函数和最简三角方程-2022年高考数学一轮复习小题多维练(上海专用)沪教版(2020) 必修第二册 同步跟踪练习 第6章 6.3.2余弦定理
解题方法
7 . 如图,四棱锥
中,底面
为矩形,
底面
,
,
,
分别为棱
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/1/b1e641bc-1e50-4f6f-946a-fd14cfad8bfe.png?resizew=197)
(1)求证:
、
、
、
四点共面;
(2)求异面直线
与
所成的角.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb7831ce178516de8ce45b05dd6401e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d783fe7f3ce673d5d21281174e7a7968.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f18a8fb41f1d09bc5791ad7fbe72593f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adc72cba412508818056817a70552176.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/1/b1e641bc-1e50-4f6f-946a-fd14cfad8bfe.png?resizew=197)
(1)求证:
![](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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
(2)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
您最近一年使用:0次
解题方法
8 . 如图,在正方体
中,点M,N分别是
,
的中点,求直线CM与
所成的角.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a696a182fff038a86b2bbe8ca099442.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1859959fdb4c5edd8056893f94a10a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9932b14d1f7f381263281a50100c27b.png)
您最近一年使用:0次
2021-12-05更新
|
149次组卷
|
4卷引用:甘肃省定西市岷县二中2017-2018学年高二下学期期中考试数学(文)试题
9 . 解下列三角方程:
(1)
;
(2)
;
(3)
;
(4)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76e5cafbb38a22857bd4428d68f33874.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/819891f70fbb52553811905b77d3a06f.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f60a981476baa1d1dfdfc3c0a67fd51d.png)
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/609bd8f28bed5760149f9c362e69200b.png)
您最近一年使用:0次
10 . 解下列三角方程:
(1)
;
(2)
;
(3)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61943a78bf6cf1bb690829890142ffb9.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bbd1776ba324df8099a366c7da8ab7e.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c8c6ab432dc40228e3da49b422700ef.png)
您最近一年使用:0次
2020-06-22更新
|
214次组卷
|
2卷引用:沪教版(上海) 高一第二学期 新高考辅导与训练 第6章 三角函数 6.11 最简三角方程(2)