1 . 如图,正方形的边长为1,
,
分别为边
,
上的动点.
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b630e42be95afffe05ebd265f9d8257b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f3d1083a956315db7b85d1e0f9aec2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4e288596fa3811dd2c17bded60e82e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9763846b1131e1e3e2d741ad95d5bb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(2)若点
![](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/030314ca026d6b18481682f70f48d19b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9763846b1131e1e3e2d741ad95d5bb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
2 . 如图,在四边形
中,
,
,
,
.
(1)若
,求
;
(2)求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7493756ad314b9026ea95b0c0282f34f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080ca48cd27d4bf9d9ef084b558fc17a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4aca5534bce25acaeb7379deed8f8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdb2dd10731b99c0f4f89ee957f8a239.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/3/a446e1f6-794d-4b4b-9928-8a0075f0c412.png?resizew=110)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a681328803cb7680ddc0d3a22d7c6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bd172042ed396eb8ff692912613fb2d.png)
您最近一年使用:0次
2023-11-10更新
|
1226次组卷
|
5卷引用:广东省肇庆市2024届高三上学期第一次教学质量检测数学试题
广东省肇庆市2024届高三上学期第一次教学质量检测数学试题专题02 解三角形(1)-【常考压轴题】(已下线)专题18 三角形中关于角的最值问题(已下线)专题12 正余弦定理妙解三角形问题和最值问题(练习)(已下线)第11章 解三角形 章末题型归纳总结(1)-【帮课堂】(苏教版2019必修第二册)
解题方法
3 . 已知椭圆
的三个顶点所确定的三角形的面积为
,
(
是
的离心率)是
上一点.
(1)求
的方程;
(2)若直线
与
交于
两点,设
,直线
与
分别交于
(不同于
)两点,当
时,记直线
的倾斜角分别为
,
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/868e60e76960c7bbecc5679d60d128c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8da73428c941022232136bdd7d0feeba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f55d12701014cf53071093e8739d089b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23418075bc5e575a773ab361010cd7a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f0d68648b10fce54dfc19c5ee60086d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84663b253587679c01af3b5cfc620661.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/f3fe9f2f9aa8d0d24bd528b7fce71b80.png)
您最近一年使用:0次
4 . 已知
的内角
所对边分别为
.若
内部有一个圆心为
,半径为
米的圆,它沿着
的边内侧滚动一周,且始终保持与三角形的至少一条边相切.
为边长是16米的等边三角形,求圆心
经过的路程;
(2)若用28米的材料刚好围成这个三角形,请你设计一种
的围成方案,使得圆心
经过的路程最大并求出该最大值(若
为正数,则
,当且仅当
时取等号).
![](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/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)若用28米的材料刚好围成这个三角形,请你设计一种
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/529b18236d8040085fea20d0bdb60c66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44acc0ee22dc4b7750e8be825e7c1355.png)
您最近一年使用:0次
2023-07-14更新
|
445次组卷
|
2卷引用:山东省潍坊市2022-2023学年高一下学期期末数学试题
名校
解题方法
5 . 已知圆
.圆D的圆心D在y轴上且与圆C外切.圆D与y轴交于A、B两点,点P为
.
(1)若点D坐标为
,求
的正切值;
(2)当点D在y轴上运动时,求
的正切值的最大值;
(3)在x轴上是否存在定点Q,当圆D在y轴上运动时,
是定值?如果存在,求出点Q坐标;如果不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/553b19083c401c2fd2486c6297a92d14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcbcd0aebdd8bd688d108834747009f5.png)
(1)若点D坐标为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb0e705301752424a492f6277ed7774e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb686e4f5e3938575bc547e849d5513f.png)
(2)当点D在y轴上运动时,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb686e4f5e3938575bc547e849d5513f.png)
(3)在x轴上是否存在定点Q,当圆D在y轴上运动时,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c7bbe0ac1c88c9d35978a7184ba553.png)
您最近一年使用:0次
名校
解题方法
6 . 在
中,角
、
、
所对的边分别为
、
、
,
.
(1)求
;
(2)若
,求
面积
的最小值.
![](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/893875c3b43d73cfcf52da867f4bb80b.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39344ad1a4a45a1023de6b5bdda76546.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cca3d220dcb6ea09400f091dcf15ca5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
您最近一年使用:0次
2023-04-15更新
|
2287次组卷
|
2卷引用:四川省达州市2023届高三二模数学(理科)试题
名校
解题方法
7 . 已知定义在
上的函数
.
(1)若曲线
在点
处的切线与两坐标轴所围成的三角形的面积为2,求k的值;
(2)将
的所有极值点按照从小到大的顺序排列构成数列
,若
成等差数列,求k的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f178aafef1a74d224f7e90f8ceeed914.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f845b89ae8c6d7c2d6566d08b9d88647.png)
(1)若曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eded821494c706422354dd910a25b1e6.png)
(2)将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b8ec9d4206ea66a02de5c4a1e1e911.png)
您最近一年使用:0次
2023-04-08更新
|
985次组卷
|
5卷引用:山西省部分学校2023届高三下学期4月模拟考试数学试题
山西省部分学校2023届高三下学期4月模拟考试数学试题吉林省四平市实验中学2022-2023学年高三下学期4月份模拟考试数学试题江苏省扬州中学2023届高三下学期阶段测试数学试题江苏省盐城市伍佑中学2023届高三高考热身考试数学试题(已下线)压轴题07三角函数与正余弦定理压轴题9题型汇总-1
名校
解题方法
8 . 如图所示是某斜拉式大桥图片,为了解桥的一些结构情况,学校数学兴趣小组将大桥的结构进行了简化,取其部分可抽象成图(1)所示的模型,其中桥塔
与桥面
垂直,通过测量得知
,当
为
中点时,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/1/8eb65219-6da9-485d-9251-edfc6794b1eb.png?resizew=383)
(1)求
的长;
(2)设
,写出
与
的函数关系式;
(3)已知命题:函数
在
内为严格增函数;求证该命题为真命题,并用该命题求解
在线段
的何处时,
达到最大,最大值为多少?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/947a9e717f8bd9e2f5eb3ba8929932a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4a3caf9045a08a8342c73496c4274cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca1d0963bbe4d4d8eda2210585fc1d7d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/1/8eb65219-6da9-485d-9251-edfc6794b1eb.png?resizew=383)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8711eddf26d11fc974dfb6da4b640918.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fbd459a6de5d294b1dfb95e596793f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(3)已知命题:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a869a76555f3369728f9005863bdb8eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4138f6987cd2ee9e56b2ac80e84f9e24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fbf1667b21a273bf5dd007d65eeda7c.png)
您最近一年使用:0次
2023-03-30更新
|
621次组卷
|
3卷引用:上海市金山中学2022-2023学年高一下学期3月素养检测(一)数学试题
上海市金山中学2022-2023学年高一下学期3月素养检测(一)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)专题12 寒假成果评价卷 -【寒假自学课】(沪教版2020)
名校
解题方法
9 . 已知椭圆
的焦距为
,离心率为
,直线
与
交于不同的两点
.
(1)求
的方程;
(2)设点
,直线
与
分别交于点
.
①判段直线
是否过定点?若过定点,求出该定点的坐标;若不过定点.请说明理由:
②记直线
的倾斜角分别为
,当
取得最大值时,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e5578ca83f5bd5c285994061b9c015.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8b44d7d5511f954ed8d59e346e265de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e9b5e076078240e0c5ad9763a9824d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ec8858389f4c3156a946ba8bf0d8a7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
①判段直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
②记直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a5f1c3d7257dd42ca1d3d77f1576313.png)
![](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/9d78abbad68bbbf12af10cd40ef4c353.png)
您最近一年使用:0次
2023-02-22更新
|
2087次组卷
|
5卷引用:山东省潍坊市2023届高三下学期一模数学试题
名校
解题方法
10 . 已知双曲线
的右焦点为F,点
分别为双曲线C的左、右顶点,过点F的直线l交双曲线的右支于
两点,设直线
的斜率分别为
,且
.
(1)求双曲线C的方程;
(2)当点P在第一象限,且
时,求直线l的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/222b4c3088d36ba0b2f5d8dedbcfc902.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/378f90fe1e622bab7a8fb2ccdc0c11cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03b8bfb1960c394ccfb7bb12de1c1b2b.png)
(1)求双曲线C的方程;
(2)当点P在第一象限,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec79607071014df4522d49f117583c42.png)
您最近一年使用:0次
2022-12-30更新
|
1688次组卷
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10卷引用:河南省百师联盟2023届高三一轮复习联考(四)全国卷理科数学试题
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