名校
解题方法
1 . 在
中,内角
的对边分别是
,且
.
(1)求角
的大小;
(2)若
,且
的面积为
,求
边上的中线长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ef0e289213adb19ea06f895c522f6a3.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/a2099b865424058d46b742a1659dafd0.png)
(1)求角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82986ab38a4ae58593191ccae2a44f62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fcb5876e83a663aa11bc213425f2345.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
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解题方法
2 . 已知
是锐角三角形,内角A,B,C所对应的边分别为a,b,
若
,则
的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/476cc89dbf8b6b3e18005800c5a3a477.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a2264c134952d41fb9bcb90e6c72c83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67b292a8835d2b23ecc22bc2097eeb4f.png)
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解题方法
3 . 在
中,内角A,B,C的对边分别为a,b,c,且
,点D是BC上靠近C的三等分点
(1)若
的面积为
,求AD的最小值;
(2)若
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f9af1804e523e12396ab876eb0ce27d.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adbd3e8cf8325999cde03adf845d3dd0.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d54e182a943f960a1885b8556d07a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e24361e4842cdaa3da819c60b55107d7.png)
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名校
4 . 已知函数
,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bda318adf65c6b6fd45f651365f52346.png)
(1)求
的最大值
(2)写出
与
的大小关系,并给出证明
(3)试问
能否作为
三边长?若能,给出证明,并探究
的外接圆的半径是否为定值?若不能,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1044dcf4fba551e1b7fbfeb895ea08c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bda318adf65c6b6fd45f651365f52346.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b692262286e03cc0536598789fab8699.png)
(2)写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88fd5c1ef0fc722337a4984834829c84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e7bb46b41cd3f1f9b5621c20bf7fe07.png)
(3)试问
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b799aaa36edd0d10fc38925ce2e55045.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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2024-06-12更新
|
163次组卷
|
2卷引用:福建省泉州市安溪第八中学2023-2024学年高一下学期6月份质量检测数学试题
5 . 已知数列
中,
,
.
(1)证明:数列
为常数列;
(2)求数列
的前2024项和.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ea8d0e50065114b05ef2dc1ea1129cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e21735689ef7272d918da315cdb5c8a.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc1e7b49d90dc3ec036367ae7567dce0.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0496f142d8ae5acb06e83526eaa3ef87.png)
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名校
解题方法
6 . 固定项链的两端,在重力的作用下项链所形成的曲线是悬链线
年,莱布尼茨等得出悬链线的方程为
,其中
为参数.当
时,该表达式就是双曲余弦函数,记为
,悬链线的原理常运用于悬索桥、架空电缆、双曲拱桥、拱坝等工程.已知三角函数满足性质:①导数:
;②二倍角公式:
;③平方关系:
.定义双曲正弦函数为
.
(1)写出
,
具有的类似于题中①、②、③的一个性质,并证明该性质;
(2)任意
,恒有
成立,求实数
的取值范围;
(3)正项数列
满足
,
,是否存在实数
,使得
?若存在,求出
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46a7e0115ce78639910150e39fdbdb0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f07f8015f0a035e80a166092be0b7318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4580cc037c0c760c728cdbb74a8154c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a7c1d3681898e25187a896aeb0c8c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf8bce35b539fdf365e9089750d4d152.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32eac4b7f177c041219fab18de973c5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9af7ca3fcd9a43d520ed650b80ef2dad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0718c04bdf70989bcc90b902671a692.png)
(1)写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a53b8e0108664bf39aa302570457199a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6e7c627427318b62d977ff7a86c2cb5.png)
(2)任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a68fd5f6e28316a932db1494deac24b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)正项数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c19bf566cd9dd81916f53ed33248197c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f816db73b759d7de72b0bd43ba39f46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ecf3a1fecf89a37a677393d0bfe27b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/805dabba8d859d870a1dfaaa9d97de41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2024-06-02更新
|
447次组卷
|
2卷引用:福建省安溪第八中学2024届高三下学期5月份质量检测数学试题
名校
解题方法
7 . 在
中,角A,B,C所对的边分别为a,b,c,请从下列条件中选择一个条件作答:(注:如果选择多个条件分别作答,则按第一个解答计分.)
①
②
③![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cd161755aa7f1e0c4313a2327cb7e7b.png)
(1)求A的大小
(2)若
为锐角三角形,求
的取值范围;
(3)若
,点A,B,C分别在等边
的边DE,EF,FD上(不含端点),若
面积的最大值为
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb639420971554d620202a8880357f3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c390057bfe42a58d0cfd4c33f095d287.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cd161755aa7f1e0c4313a2327cb7e7b.png)
(1)求A的大小
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99ea513ef4c8fc4d8c31eff498740680.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5742b2684d00be50a66e01c9acb6b51f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72cb97395ebc5ee1b212afb7a97b985c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72cb97395ebc5ee1b212afb7a97b985c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e56e21a9e25f762fbf4b1a143b128aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
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名校
解题方法
8 . 已知锐角
中,内角
,
,
的对边分别为
,
,
,若
,且
,
(1)求
;
(2)若
为
边上的高,过点
分别作边
、
的垂线,垂足分别为
、
,
(ⅰ)求证:
;
(ⅱ)求
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/8fac8bafb7fc055d3ac713b9da7fba4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2171425a65374b6e7b68d4e9a3008795.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
(ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b8a2842414dac8edc367cffea4110d9.png)
(ⅱ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
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2024-05-25更新
|
535次组卷
|
2卷引用:福建省厦门市第一中学2023-2024学年高一下期中考试数学试卷
名校
解题方法
9 . 记
的内角
的对边分别为
.已知
,则
的取值范围为__________ .
![](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/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a92cfa82ed0e7652b482635e72a84ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc940e481607daedc1e83e98ec3bd4c0.png)
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解题方法
10 .
中,内角
、
、
的对边分别为
、
、
,且
.
(1)若
,试判断
的形状,并说明理由;
(2)若
,则
的面积为
,求
,
的值;
(3)若
为锐角三角形,求
的取值范围.
![](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/fa2f9aa3afe9f50954d9bc787a8a2ce8.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ae7e59e7d1e6814416c15d8abaa8d3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03837b3769eda7f0d3804cc5ad4a6d60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a8080fef9bdfa92ae70f3e314eef3e3.png)
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2024-05-08更新
|
599次组卷
|
3卷引用:福建省福州市第十五中学等五校2023-2024学年高一下学期期中联考数学试题
福建省福州市第十五中学等五校2023-2024学年高一下学期期中联考数学试题河南省驻马店市新蔡县第一高级中学2023-2024学年高一下学期5月月考数学试题(已下线)专题05 解三角形大题常考题型归类-期期末考点大串讲(人教B版2019必修第四册)