锐角
ABC的内角A,B,C的对边分别为a,b,c,已知
.
(1)证明:
.
(2)求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4cba95fc7d4853a243f8e3fb20ce70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7c7ca096c1f922d1b5f1b2eb8bee12b.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e620a0ef4c8a7e05bfb1d7248a3c823.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2122e3f1e76a635e58e4d54aa594c552.png)
23-24高三上·江苏·阶段练习 查看更多[3]
江苏省百校大联考2024届高三上学期第二次考试数学试题重庆市九龙坡区杨家坪中学2024届高三上学期第五次月考数学试题(已下线)第16讲 第六章 平面向量及其应用 章末重点题型大总结(2)-【帮课堂】(人教A版2019必修第二册)
更新时间:2023-12-13 19:14:43
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【推荐1】定义非零向量
的“相伴函数”为
,
,向量
称为函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abc54bc56c16baa3643686b85a6130e4.png)
的“相伴向量”(其中点
为坐标原点).
(1)设函数
,求函数
的“相伴向量”
的坐标;
(2)记
的“相伴函数”为
,设函数
,
,若方程
有四个不同实数根,求实数k的取值范围;
(3)已知点
,
满足条件:
,且向量
的“相伴函数”
在
时取得最大值,当点M运动时,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074d049ba730bc0a038a076d5eb10035.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abc54bc56c16baa3643686b85a6130e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31ece875d11d850450d28acfafb7bec6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074d049ba730bc0a038a076d5eb10035.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abc54bc56c16baa3643686b85a6130e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31ece875d11d850450d28acfafb7bec6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(1)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e95a5f3ef304ee910dc162c999672c66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b6799b234237333b0efa331d98f0374.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e936e203fb157e941e926a8cf8a71980.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/093d3ad8f1284ef33b5a174ec57fb68e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37440b57fe2ffc13f2a873e38f55d29b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19d3d7b48ea2c4a0c74ebfb263c4eeb2.png)
(3)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2d6bb01f1044358cc5fee441bc62489.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f0254507d80b7475e7ba9d5e043a1bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bec0705d808bfdd465aa1b585acb628.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b6799b234237333b0efa331d98f0374.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11abb76da45ffa52b47c3a6b9a03ac7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63e0e24323fe73e5d9fc6136219306da.png)
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【推荐2】已知函数
的最小正周期为
.
(1)求
的解析式及对称轴方程;
(2)若关于x的方程
在
上有两个不等实数解
,
.
①求实数m的取值范围;
②求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18a73c9015d26b93d542a271da093dae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70f5389990c3a0c5373f3bd9fb2454c9.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若关于x的方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c05885b987fc9a9d54574896cf2efec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44d51992c05a557cf6058664f1f8961e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
①求实数m的取值范围;
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40c320ac1e6528e865a73a0b5fed9408.png)
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【推荐1】△ABC的内角A,B,C所对的边分别为a,b,c.已知
且
.
(1)求角B;
(2)若D为AC边的中点,且
,求△ABC的面积
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0e1f861b1aae4486e30e6b730fbfe0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6de1d395e6c48c0676a1488a299479d9.png)
(1)求角B;
(2)若D为AC边的中点,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b77f1b9b728f39d0d9618504567eeb96.png)
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【推荐2】在
中,
分别为角
所对的边,且满
.
(1)求角
的大小;
(2)若
,求
的周长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53f7f71be5e6ab27be49c4d9a45d54f5.png)
(1)求角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/432e1bef51c4d2e9107b28ca3f1d3acf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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【推荐1】在锐角△ABC中,角A,B,C所对的边分别为a,b,c,已知
,且
.
(1)求证:
;
(2)若
的平分线交AC于D,且
,求线段BD的长度的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07ac99c98d7fd621dbb6595d824c28cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/098943e98ad321740f83f0bb67004598.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f44c181a2f6ae22d5d52b374768dc57.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39b8d91afc34e4a9b0fdbb6bafb9087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22a688b51f4862f610d3064199aeb336.png)
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【推荐2】已知函数
,
(1)求函数
的最小正周期及单调递增区间;
(2)若在锐角
中,已知函数
的图象经过点
,边
,求
周长的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1b0294d43bc95b51dfcbb7209639285.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若在锐角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52e297dd61553ea887d6a6f464331d99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f656e1d1f68954e5f06de8958f6a9310.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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