2024高一下·上海·专题练习
名校
解题方法
1 . 如图,
,
是单位圆上的相异两定点
为圆心
,且
为锐角
点
为单位圆上的动点,线段
交线段
于点
.
结果用
表示
;
(2)若
.
①求
的取值范围;
②设
,记
,求函数
的值域.
![](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/bd109d3cea698760b0d5edb65bd6f241.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef8fbf1acaacf8e9bb3aff495d4f732a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/913b7537e011acfeec11952731351388.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36df2ad9c36e4df0d626f2618e842abe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f72bf0fce80daad394f2a9d013829c5c.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6da9ea780ba5e54f3be57b4a7bb12b1.png)
②设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55c52debaee90830375fbfd15cf1ea35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7efab43171f12140ce67bb974f203d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acb17843c51402a1f7cd9b07542597b9.png)
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2024-04-10更新
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3卷引用:第八章 平面向量(压轴题专练)-单元速记·巧练(沪教版2020必修第二册)
(已下线)第八章 平面向量(压轴题专练)-单元速记·巧练(沪教版2020必修第二册)广东省佛山市顺德区华侨中学2023-2024学年高一下学期3月月考数学试卷重庆市第八中学校2023-2024学年高一下学期4月阶段练习数学试题
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解题方法
2 . 已知
,其中
,
都是常数,且满足
.
(1)当
,
时,求
的取值范围;
(2)是否存在
,
,使
的值是与
无关的定值?若存在,求出
,
的值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/532a8c3a44b1fab73dff11ddd96f84f6.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/ce86a9b5b4401c1b43ae52333e19b2c5.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ea81da7f8471a097675421508bb5f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1291e6ed6d42d5f71625ba7bca78b686.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5224a7da7fe6bc28971ce4c277f88588.png)
(2)是否存在
![](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/5224a7da7fe6bc28971ce4c277f88588.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
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2024高一下·上海·专题练习
名校
3 . 对于集合
和常数
,定义:
为集合
相对
的“余弦方差”.
(1)若集合
,
,求集合
相对
的“余弦方差”;
(2)求证:集合
,相对任何常数
的“余弦方差”是一个与
无关的定值,并求此定值;
(3)若集合
,
,相对任何常数
的“余弦方差”是一个与
无关的定值,求出
、
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0e94af231799820b1b50e80dd38b869.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a4438bae1705c0f26beddf41322c087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89087b5832048b3f67075371253e5fb4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a4438bae1705c0f26beddf41322c087.png)
(1)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b9f7dba284b1f15b1660db9875bdada.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35272ddbd63d2485769020d9839445f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a4438bae1705c0f26beddf41322c087.png)
(2)求证:集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a2a8f4e2a2972da8e72c7aa3e8ce91d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a4438bae1705c0f26beddf41322c087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a4438bae1705c0f26beddf41322c087.png)
(3)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5dfea362ad666e61cf04e2768215d2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a45cb3486e8835fa7b848e51b53043fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a4438bae1705c0f26beddf41322c087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a4438bae1705c0f26beddf41322c087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
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549次组卷
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8卷引用:第六章 三角(压轴题专练)-单元速记·巧练(沪教版2020必修第二册)
(已下线)第六章 三角(压轴题专练)-单元速记·巧练(沪教版2020必修第二册)上海民办南模中学2023-2024学年高一下学期期中考试数学试卷(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)(已下线)第10章 三角恒等变换 单元综合测试(难点)-《重难点题型·高分突破》(苏教版2019必修第二册)(已下线)第八章:向量的数量积与三角恒等变换章末重点题型复习(2)-同步精品课堂(人教B版2019必修第三册)山东省青岛第五十八中学2023-2024学年高一下学期3月月考数学试卷广东省惠州市第一中学2023-2024学年高一下学期第一次阶段考试数学试题(已下线)专题04 三角函数恒等变形综合大题归类 -期末考点大串讲(苏教版(2019))
名校
4 . 已知函数
,
,若方程
在区间
内无解,则
的取值范围是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3474a6bdb7fd647ebbf15ae318c98b37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6889205677dfb9a02934c36088b75d7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3047d4ab078dafc06c047bcbf0a6ffaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe386ad25a4c1cce633ed4e129127047.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
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解题方法
5 . 如图,有一块扇形草地
,已知半径为R,
,现要在其中圈出一块矩形场地
作为儿童乐园使用,其中点A,B在弧
上,且线段
平行于线段
;
(1)若点A为弧
的一个三等分点,求矩形
的面积S;
(2)设
,当A在何处时,矩形
的面积S最大?最大值为多少?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e17dc84ba2e871aeb3a3fd2a2b5f1a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28986ee88e684ebb6020d5f69047ccb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/6/f52447bc-8850-441b-b211-27faf6aca7a7.png?resizew=201)
(1)若点A为弧
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2b1cf570968108d18d4a3cca50368a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
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2023-08-05更新
|
929次组卷
|
5卷引用:上海市市北中学2022-2023学年高一下学期期中数学试题
上海市市北中学2022-2023学年高一下学期期中数学试题(已下线)7.1 正弦函数的图像与性质-高一数学同步精品课堂(沪教版2020必修第二册)(已下线)专题14 三角函数的图象与性质压轴题-【常考压轴题】江西省赣州市第四中学2023-2024学年高二上学期开学考试数学试题河南省南阳市邓州市第六高级中学校2023-2024学年高二下学期开学测试数学试题
名校
6 . 已知矩形
的边
,点
分别在边
上,且
.
(1)若
,求
的面积;
(2)求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c79e56bc6f1db8f446fc5bd34a08865.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/481e426224c3a3ce9bb5a731eed81c40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9a2441279907a130e42dec796f5fa63.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/22/8a5cced7-7eac-42d4-ae5f-66c4807e49ab.png?resizew=163)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40ecff1763ef7514d3ef5b4c53de572c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c499b1f470978c4f8cc05ffdebc2e961.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc5604d3e156df3e7ccca0ccec9c9d45.png)
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解题方法
7 . 若a、b为实数,且
,函数
在闭区间
上的最大值和最小值的差为1,则
的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a46e678bf9d2df5ad4c782b3dc22f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2b9643da0c0fea4f099f9a9133d6076.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13502d46b8563c54c09b29b20b3006a4.png)
您最近一年使用:0次
2023-06-05更新
|
958次组卷
|
4卷引用:上海市大同中学2023-2024学年高一下学期期中考试数学试卷
上海市大同中学2023-2024学年高一下学期期中考试数学试卷上海市大同中学2023届高三三模数学试题(已下线)专题06 三角函数的图像与性质(已下线)第四章 三角函数与解三角形 第三节 三角恒等变换 第二课时 简单的三角恒等变换(B素养提升卷)
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8 . 已知函数
,若存在实数m、k(
),使得对于定义域内的任意实数x,均有
成立,则称函数
为“可平衡”函数;有序数对
称为函数
的“平衡”数对.
(1)若
,求函数
的“平衡”数对;
(2)若m=1,判断
是否为“可平衡”函数,并说明理由;
(3)若
、
,且
、
均为函数
的“平衡”数对,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0baedc4d7e690ab3f7d80d30ba0a9efe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e76b43fa87a022251c67fd1aba814f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efa6e6840235cbfe76f9827fc755d4cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b1c079afd1b058adc67a50f48f3d466.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若m=1,判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1044dcf4fba551e1b7fbfeb895ea08c.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77ab1256702aef4e9f1a5eb6c12ecc96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a381e6a27606c6856cc5e9ba0255310.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e8ed078c2a52840d52df47bc09ed5b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d5b8e084e08f8def509f3fd49639b97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14f125b3065bc6bb1c92227ca64b6260.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5ce92f59ccf725aeed263923f2e7082.png)
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2023-05-13更新
|
1095次组卷
|
14卷引用:上海市奉贤中学2022-2023学年高一下学期期中数学试题
上海市奉贤中学2022-2023学年高一下学期期中数学试题(已下线)6.2 常用三角公式-高一数学同步精品课堂(沪教版2020必修第二册)上海市闵行区六校联考2023-2024学年高一下学期4月期中质量调研数学试题(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)(已下线)高一下册数学期末模拟卷(三)-【超级课堂】湖南省株洲市炎陵县2022-2023学年高一下学期6月期末数学试题河南省南阳市方城县2022-2023学年高一下学期期末数学试题江苏省盐城市建湖高级中学2023-2024学年高一下学期开学情检测数学试题(竞赛班)(已下线)第10章 三角恒等变换 单元综合测试(难点)-《重难点题型·高分突破》(苏教版2019必修第二册)山东省胶州市第一中学2023-2024学年高一下学期3月月考数学试题湖北省武昌实验中学2023-2024学年高一下学期3月月考数学试卷广西南宁市第三中学2023-2024学年高一下学期月考(二)数学试题(已下线)专题22 新高考新题型第19题新定义压轴解答题归纳(9大题型)(练习)辽宁省沈阳市东北育才学校双语校区2023-2024学年高二下学期4月自主测评数学试题
名校
9 . 已知函数,(其中
,
)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5095a28bb1b91bf6bed9e2cfbd76bb18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5095a28bb1b91bf6bed9e2cfbd76bb18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34ee7c9b6c99c07c4299cbaf957317ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/572bcf8a6fa788eb7fce7532a406fed1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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名校
解题方法
10 . 已知
中,角A,B,C的对边分别是a,b,c,下列命题中,真命题的个数是( )
(1)若
,则
是等腰三角形;
(2)若
,则
是直角三角形;
(3)若
,则
是钝角三角形;
(4)若
,则
是等边三角形.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd7ec9f2a433a1fe1975b221025a4be5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/397fca77f42d61ad3ff5388cee5bf80e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd1116215e558396687e4ca6fc8bbabf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(4)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f751796ea4ad7c937292060d1c113f7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
A.1 | B.2 | C.3 | D.4 |
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