1 . 化简下列各式:
(1)
.
(2)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bc9461b42cae9d7f2b93795de3f328a.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/325dd58d4bb86b0cf31464cda0943d0d.png)
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解题方法
2 .
的角
对应边是 a,b,c ,三角形的重心是 O.已知
.
(1)求 a 的长.
(2)求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9fbd659c7e4424a2ea5a20a86c0cf7.png)
(1)求 a 的长.
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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3 . 在
中,角
所对的边分别为
,且
.
(1)求
的大小;
(2)若
,
,点
在边
上,且
,求线段
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e428e7a09732be85c1224e9c8f6a71c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/681d30b8ee9f223a379684ccc6ef7375.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b71812e0762c0aaffb51cfef66156567.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6de1d395e6c48c0676a1488a299479d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a372560e41dbe1a873ac4e75b2a7892.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
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2024-05-04更新
|
831次组卷
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3卷引用:广东省东莞市东莞中学2023-2024学年高一下学期第一次段考数学试题
名校
4 . 在
中,内角
,
,
的对边分别为
,
,
.已知向量
,
,且
.
(1)求角
的大小;
(2)若
,
,求
的面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.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/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5f98a1d74c832a09544fac815c39c53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d03f4ae14627390a09bba0223c342c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a4d070c5939bb0ec4a9d40d7e3c7d3f.png)
(1)求角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b2b7db8565506b92293f4a15ec9e61e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30b6afafae50d87d0ecf3ae0e0103b0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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2024-04-26更新
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520次组卷
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3卷引用:贵州省毕节市金沙县实验高级中学2023-2024学年高一下学期第一次月考数学试题
5 . (1)化简下列各式:
①
;
②
.
(2)已知向量
,
,
与
的夹角为
.
①求
;
②求
.
(3)已知向量
,
.
①求
;
②若
,求实数
的值.
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4074b93ead6f32e784576801e5193c00.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4bb22718194f581c971f54e7bc2e77a.png)
(2)已知向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29276b43a2950ed71f0f9629a35dfa74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2396cac4b185cf1f1a67dad9248481c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1a63ab608517bb10aa036783dfb51f.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/854e16eb319ee454088f5b527cf6c4d5.png)
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93af88a7628c71d642d3a6df067c15f5.png)
(3)已知向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5463fb0b7d03747aa4d680620ca81be2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aabefecd4de8455e21919d34005588f.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08e6f98f23fea7db0f74897928024ca0.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25d209e529faa74004ca556cf3d6b321.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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6 . 已知在
中,N是边AB的中点,且
,设AM与CN交于点P.记
.
表示向量
;
(2)若
,且
,求
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42ee071eeac50f0aad26a5139fdf2a1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8cc47326e366b5b07350d461bf75474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b901cc29a51575d40f331c7b9b1e696f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75b2f1f3c3a1e6f78e384193b1d07962.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80d98c4bb451306e711fd5e2fed99487.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f64ecaa4ed6aecefc9e26932e528596c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67dfcdf2fcb1c69e286634cb9405781e.png)
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2024-04-10更新
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984次组卷
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3卷引用:江苏省扬州市广陵区红桥高级中学2023-2024学年高一下学期3月月考数学试题
7 . 在
中,已知
,
,
.
(1)若
为
边上的中线,求
的长度;
(2)若
平分
,且
点在
上,求
的长度.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8a7b5adfcac0f46a4cd19da4ebb4a2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e899c486dc49e560fc4aca05e16835b7.png)
(1)若
![](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/03902478df1a55bc99703210bccab910.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cbce11aa19b8bd2bf6ee5a834e005de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
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8 . 已知向量
,
,非零向量
(其中
、
).
(1)当
,
时,
,求
的值;
(2)当
时,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d543813f240d677c8380afb0363eef96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/267fdb24e7345bd8f772d3cec3c4b217.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/385495ec3ecd33e95b9b671ccc2866b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3276b5e12396fc4753eb3f8254f9fa68.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e94f16d5ed858699bfea5039a7bf8ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4561e662151983a27b3e8c8fcc857f06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba4d488d56b95a44a6b0b40d3e89c010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63de2843f4cd42c95ccba0a9039e002a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/136fbf7f9e6ed0fbbca15df33d779a72.png)
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解题方法
9 . 在直角梯形
中,已知
,
,
,动点
、
分别在线段
和
上,且
,
.
时,求
的值;
(2)求向量
的夹角;
(3)求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f864244952b60f3648f08a19268efae9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9060f03b9ee41d70d135b1e1a8902ce9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/109848fe67e9e9e0989e02777f8bbbb7.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/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/689a912bada8ad9041f352c6b4baa182.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e845d8f5a7ee88e1c402a108a8ffb64f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/441809d6ce2df21a85b390cdce9b1112.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7700cb2566526a121b5dcd25b8d9f10e.png)
(2)求向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46b5ba2783b42aa3908ac4bf71c5bb39.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3c742e7006441e4106692ddad15d07.png)
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2024-03-21更新
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1815次组卷
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6卷引用:江苏省常州市联盟学校2023-2024学年高一下学期3月学情调研数学试卷
名校
解题方法
10 . 设a,b,c分别为
内角A,B,C的对边,已知
,
.
(1)求A的值;
(2)若
,
,求c的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03837b3769eda7f0d3804cc5ad4a6d60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/621f0f565c473d7f14a912acd2191e66.png)
(1)求A的值;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d253dd9af597ae29b98628f185eb447.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb0786732df29e599cd67cd69e5a1a5f.png)
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2024-03-03更新
|
551次组卷
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4卷引用:云南省楚雄彝族自治州2024届高三上学期期末数学试题