名校
1 . 在
中,三内角
所对的边分别是
,若
依次成等比数列,
则
的取值范围是____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38335830b93ac4d99c28a8e209eecb3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
则
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9ed77048c6f38345bf14e1ccb526fe1.png)
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名校
2 . 某小区拟对如图一直角△ABC区域进行改造,在三角形各边上选一点连成等边三角形
,在其内建造文化景观.已知
,则
面积最小值为____
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72cb97395ebc5ee1b212afb7a97b985c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/def073bb68959ab3befba5c1550eb170.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72cb97395ebc5ee1b212afb7a97b985c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/7/77f85e2e-b506-417a-9ce8-969772724bdc.png?resizew=173)
您最近一年使用:0次
2019-05-29更新
|
1318次组卷
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2卷引用:【市级联考】贵州省遵义市2018-2019学年高一下学期期中考试数学试题
3 . 有一解三角形的题,因纸团破损有一个条件不清,具体如下:在
中,已知
,
,__________ 求角
经推断破损处的条件为三角形一边的长度,且答案提示
,试将条件补充完整.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8120119749d4bc28067e73fca7d46cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dd7dd92ecaa6d218ee984b4be92b115.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0ebd06e89654d96d8a7b44905e89e38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99f2f1eb2beb23690f56a68dc7da08cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
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2021-08-15更新
|
596次组卷
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3卷引用:贵州省贵阳市民族中学2020-2021学年高一下学期第一次月考数学试题
解题方法
4 . 定义函数
为“正余弦”函数.结合学过的相关知识,我们可以得到该函数的性质:
1.我们知道,正弦函数
和余弦函数
的定义域均为
,故函数
的定义域为
.
2.我们知道,正弦函数
为奇函数,余弦函数
为偶函数,对
,
,可得:函数
为偶函数.
3.我们知道,正弦函数
和余弦函数
的最小正周期均为
,对
,
,可知
为该函数的周期,是否是最小正周期呢?我们继续探究:
.可得:
也为函数
的周期.但是否为该函数的最小正周期呢?我们来研究
在区间
上的单调性,在区间
上,余弦函数
单调递减,正弦函数
在
上单调递增,在
上单调递减,故我们需要分这两个区间来讨论.当
时,设
,因正弦函数
在
上单调递增,故
,令
,
,可得
,而在区间
上,余弦函数
单调递减,故:
即:
从而,
时,函数
单调递减.同理可证,
时,函数
单调递增.可得,函数
在
上单调递减,在
上单调递增.结合
.可以确定:
的最小正周期为
.这样,我们可以求出该函数的值域了:显然:
,而
,故
的值域为
,定义函数
为“余正弦”函数,根据阅读材料的内容,解决下列问题:
(1)求该函数的定义域;
(2)判断该函数的奇偶性;
(3)探究该函数的单调性及最小正周期,并求其值域.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51e993b08ed5a326d30a133fee93ed96.png)
1.我们知道,正弦函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2b9643da0c0fea4f099f9a9133d6076.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58c65d71e57e6e7697e2f627dcd58583.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51e993b08ed5a326d30a133fee93ed96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
2.我们知道,正弦函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2b9643da0c0fea4f099f9a9133d6076.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58c65d71e57e6e7697e2f627dcd58583.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51e993b08ed5a326d30a133fee93ed96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5562150b6fe45dc60e7790685d5cb0a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51e993b08ed5a326d30a133fee93ed96.png)
3.我们知道,正弦函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2b9643da0c0fea4f099f9a9133d6076.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58c65d71e57e6e7697e2f627dcd58583.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e9fdc1f8ed0ae44b54a9a2a3aca2db4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51e993b08ed5a326d30a133fee93ed96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95905e2ad46af324ee4035edde8d69fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e9fdc1f8ed0ae44b54a9a2a3aca2db4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/222443a4830f8e17589afbcd3b5ea8c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86ebba6ed1add0fe647c0226614b9290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51e993b08ed5a326d30a133fee93ed96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51e993b08ed5a326d30a133fee93ed96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1613d377a07850c72cbec354b7a3000f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1613d377a07850c72cbec354b7a3000f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58c65d71e57e6e7697e2f627dcd58583.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2b9643da0c0fea4f099f9a9133d6076.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18c9aeed3c8c5a04e48d011c607f9142.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/987f14be6c8eafc1e87b74cbfc8ec724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ce485410257c9c1fae9d87ce3e44cc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/268bc75afffcf150cd2d275d61d36db5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2b9643da0c0fea4f099f9a9133d6076.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18c9aeed3c8c5a04e48d011c607f9142.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4d8084889c29e867974276d7f6cc476.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22f9e38660fee00a21e4216453cef349.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ab0957ab234a30417941f39466bb20c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4718dc8a3682110b1eaf18c71f6411be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1613d377a07850c72cbec354b7a3000f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58c65d71e57e6e7697e2f627dcd58583.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/839783e6263b1078fb6ed58ea70091a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9d47e9cb5749b486474f210c407afc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ce485410257c9c1fae9d87ce3e44cc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51e993b08ed5a326d30a133fee93ed96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6895733d1e3b807a8d774ae70dc897e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51e993b08ed5a326d30a133fee93ed96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51e993b08ed5a326d30a133fee93ed96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18c9aeed3c8c5a04e48d011c607f9142.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/987f14be6c8eafc1e87b74cbfc8ec724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35263c6f9845207fca5862101815e931.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51e993b08ed5a326d30a133fee93ed96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86ebba6ed1add0fe647c0226614b9290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbc02e7c12d8bec64f97adadbbf0e2da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddde153cb6c0f7a212171b6b4bbf74ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51e993b08ed5a326d30a133fee93ed96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2546805fbe7c56c33a7a91f3d9691247.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8823f10e09d28d63d87941099ddb621e.png)
(1)求该函数的定义域;
(2)判断该函数的奇偶性;
(3)探究该函数的单调性及最小正周期,并求其值域.
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名校
5 . 已知函数
,将
的图象上所有点的横坐标变为原来的
倍(纵坐标不变),再将图象向左平移
个单位,所得图象对应的函数为
,若函数
的图象在
,
两处的切线都与x轴平行,则
的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0dafcc4dec2d6831cff028c9adffff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.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/f82358b724051b032c7ec734a226ae84.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2019-12-31更新
|
1152次组卷
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8卷引用:贵州省兴义市第八中学2020届高三第七次月考数学试题
贵州省兴义市第八中学2020届高三第七次月考数学试题云南省昆明市云南师范大学附属中学2019-2020学年高三适应性月考卷(五) 文科数学试题云南省昆明市云南师范大学附属中学2019-2020学年高三适应性月考卷(五) 理科数学试题云南省师范大学附属中学2019-2020学年高三上学期第五次月考数学(文)试题云南省师范大学附属中学2019-2020学年高三上学期第五次月考数学(理)试题重庆市渝中区巴蜀中学校2020届高三下学期2月月考(理科)数学试题2020届四川省成都市棠湖中学高三3月考试(网络)理科数学试题(已下线)专题03 三角(第一篇)-备战2020高考数学黄金30题系列之压轴题(新课标版)
6 . 在数1和2之间插入
个正数,使得这
个数构成递增等比数列,将这
个数的乘积记为
,令
,
,
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3468a665ac713ab7b400c672f19650a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3468a665ac713ab7b400c672f19650a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f51d87e81c4d7c2df9f7bf9fe9fa31f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e5c3dfa276f2032f32083d8dd6d6b10.png)
您最近一年使用:0次
解题方法
7 . 在推导很多三角恒等变换公式时,我们可以利用平面向量的有关知识来研究,在一定程度上可以简化推理过程.如我们就可以利用平面向量来推导两角差的余弦公式:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e6276ff5468f5aa9c6eaff479c26cc7.png)
具体过程如下:
如图,在平面直角坐标系
内作单位圆O,以
为始边作角
.它们的终边与单位圆O的交点分别为A,B.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/3378e1b0-11ac-4e21-89d7-e7bef545c1e9.png?resizew=334)
则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a98717138350884b83b2bc3335ac3262.png)
由向量数量积的坐标表示,有:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/437ebce60a1d755209353f0d94462154.png)
设
的夹角为θ,则
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/665d77a90728ca9eb4d63b07dbe89e80.png)
另一方面,由图3.1—3(1)可知,
;由图可知,
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/8e003e58-f755-4f57-ba40-42e3c44c2f0e.png?resizew=348)
.于是
.
所以
,也有
,
所以,对于任意角
有:
(
)
此公式给出了任意角
的正弦、余弦值与其差角
的余弦值之间的关系,称为差角的余弦公式,简记作
.
有了公式
以后,我们只要知道
的值,就可以求得
的值了.
阅读以上材料,利用下图单位圆及相关数据(图中M是AB的中点),采取类似方法(用其他方法解答正确同等给分)解决下列问题:
(1)判断
是否正确?(不需要证明)
(2)证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/889623d5e61054f38a35aedd644c9ff5.png)
(3)利用以上结论求函数
的单调区间.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e6276ff5468f5aa9c6eaff479c26cc7.png)
具体过程如下:
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/c3e5af20b2f8c1fba4470f9650989e51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfa404d3ff313b0a28a76a48d7d87234.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/3378e1b0-11ac-4e21-89d7-e7bef545c1e9.png?resizew=334)
则
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a98717138350884b83b2bc3335ac3262.png)
由向量数量积的坐标表示,有:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/437ebce60a1d755209353f0d94462154.png)
设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/538844ce819df320039e394ba92356f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/665d77a90728ca9eb4d63b07dbe89e80.png)
另一方面,由图3.1—3(1)可知,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/655ee7e11f540619722504916419e009.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/8e003e58-f755-4f57-ba40-42e3c44c2f0e.png?resizew=348)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18eedcc65589e7529da85a578bd0ecb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e366809cf946d825277ad151abb374a2.png)
所以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a689c643b92f5fafe77fb2c754b0184.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e6276ff5468f5aa9c6eaff479c26cc7.png)
所以,对于任意角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4e288596fa3811dd2c17bded60e82e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e6276ff5468f5aa9c6eaff479c26cc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9e74ca761ffa2566a9851c5ce9ccaaf.png)
此公式给出了任意角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4e288596fa3811dd2c17bded60e82e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd927b4b5a7875528c1b54aa4bb8b2dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9e74ca761ffa2566a9851c5ce9ccaaf.png)
有了公式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9e74ca761ffa2566a9851c5ce9ccaaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1455db71a4123b3317dcfce3e2005e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22d521f8d021b20757d7a68107fcef1d.png)
阅读以上材料,利用下图单位圆及相关数据(图中M是AB的中点),采取类似方法(用其他方法解答正确同等给分)解决下列问题:
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90f93aa4ff886e380c9b7c05dbafd08d.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/889623d5e61054f38a35aedd644c9ff5.png)
(3)利用以上结论求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1414c4eb3a476aac49f6a35d62b1f7ac.png)
您最近一年使用:0次
2020-05-22更新
|
713次组卷
|
3卷引用:贵阳市普通高中2018-2019学年度高一上学期数学期末质量监测试题
贵阳市普通高中2018-2019学年度高一上学期数学期末质量监测试题贵州省贵阳市2018-2019学年高一(上)期末数学试题(已下线)大题好拿分期中考前必做30题(压轴版)-2020-2021学年高一数学下册期中期末考试高分直通车(沪教版2020必修第二册)
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8 . 已知函数
,设其最小值为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01b3ae7e5228fd1acb0d46f6941143a7.png)
(1)求
;
(2)若
,求a以及此时
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fdac28c4c4436ae735bbf02271bb29d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01b3ae7e5228fd1acb0d46f6941143a7.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01b3ae7e5228fd1acb0d46f6941143a7.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/982ecaa2793a1b8fc2c4596f3b9a506c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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2019-09-18更新
|
1067次组卷
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4卷引用:贵州省六盘水市第二中学2019-2020学年高一上学期12月月考数学试题
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9 . 已知函数
,给定以下命题:
①
为偶函数;②
为周期函数,且最小正周期为
;③若
,则
恒成立.
正确的命题个数为个.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbcaf15f2edb089f80a41b3d9a7c3c0.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e9fdc1f8ed0ae44b54a9a2a3aca2db4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e33862fa39040863f9ffa2975dedde2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/018857ec6e498113b3b12a730d9313da.png)
正确的命题个数为个.
A.0 | B.1 | C.2 | D.3 |
您最近一年使用:0次
2019-10-12更新
|
928次组卷
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3卷引用:2019年贵州省铜仁市第一中学高三上学期第二次模拟考试数学试题(理科)
2019年贵州省铜仁市第一中学高三上学期第二次模拟考试数学试题(理科)2020届贵州省铜仁第一中学高三上学期第二次模拟数学(理)试题(已下线)专题07 《三角函数》中的恒成立问题-2021-2022学年高一数学上册同步培优训练系列(苏教版2019)
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10 .
内角A、B、C的对边分别是a、b、c,已知:
.
(1)求
;
(2)若
边上的中线BD长为
,求
面积;
(3)
,求
内切圆半径的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0706f95070c2f8b197baebd3462507fb.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e945ce61be2a8e16d8022a79ec4b8ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50690dab38f4512eb72e18b7f86cf6f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8120119749d4bc28067e73fca7d46cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
您最近一年使用:0次