名校
解题方法
1 . 在圆锥PO中,AC为底面直径,
为底面圆O的内接边长为
的正三角形,点E为PC中点,且母线PC与底面圆O夹角为
.
(1)求证:平面
平面
.
(2)求二面角
的平面角的正弦值.
(3)在PO上是否存在点M,使得DM与平面
所成角为
,若存在,请求出所在位置;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1a63ab608517bb10aa036783dfb51f.png)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3547a914468b082d8d8741b974a03190.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abd284f76d9f5769bc189508ce2572b.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98e384e0ffc3d599303b77ee2a12221e.png)
(3)在PO上是否存在点M,使得DM与平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1a63ab608517bb10aa036783dfb51f.png)
您最近一年使用:0次
名校
2 . 代数基本定理:任何一个
次复系数多项式方程
至少有一个复根.由此可得如下推论:
推论一:任何一元
次复系数多项式
在复数集中可以分解为
个一次因式的乘积;
推论二:一元
次多项式方程有
个复数根,最多有
个不同的根.即一元一次方程最多有1个实根,一元二次方程最多有2个实根等.
推论三:若一个
次方程有不少于
个不同的根,则必有各项的系数均为0.
已知
.请利用代数基本定理及其推论解决以下问题:
(1)求
的复根;
(2)若
,使得关于
的方程
至少有四个不同的实根,求
的值;
(3)若
的图像上有四个不同的点
,以此为顶点构成菱形
,设
,
,求代数式
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ab009a153dfcc13ba9eb4916c76f8ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b7bff9b2431134f7683a9cc4e68acd.png)
推论一:任何一元
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ab009a153dfcc13ba9eb4916c76f8ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
推论二:一元
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
推论三:若一个
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0876215b2fd463d151523cd3c6b447.png)
已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b14c686bfce270ec65d068555d1866ff.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dadabea3f5008d97a32382752e62bdd8.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ec4e65c4c043edef8084b292675395c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcecb855c13987b207aec2db73c9ec5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c82a10b4f0c9323d726804c89dd9548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fc04eee630e386f7be4ac709ff4e16c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df74fc4cedb204eb6dcce64b706e99c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed0c942fae0e9dd2d219ad8269511898.png)
您最近一年使用:0次
名校
解题方法
3 . 在棱长为2的正方体
中,E,F,M,N分别为
,
,
,
中点.
(1)求证:
平面
;
(2)求直线
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e619f087b6b7ab764362b8b64b220cd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3182db896bc2462331796e2a6108363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc65c549059934e69355d8ecc245da57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f257d6a77d394ddca1f825559aadd5be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3225b8916372c7e0e4d7b71b26571e8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/6/17/8ea83e69-f4b4-44da-a585-6110ad87a320.png?resizew=166)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/073a88b42836fb88433679932b48ad03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72bdc4f7de61cf83503ccb8a81b36c47.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0215e13a9fb5574d5194aeb9507a98aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6b686178c52fdf7ac270e75c0795417.png)
您最近一年使用:0次
名校
解题方法
4 . 在
中,内角
所对的边分别为
,已知
,
.
(1)求
.
(2)若
为锐角三角形,求
面积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce7af7c5df749c6fa9bbe87faa72c66d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88f2599ca8b6b683e57a82699c8b1ebb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/759e6d90078d6d79e68c55e39e118d78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2129fc59f4fbcc28ac8ea3df9c550eac.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
您最近一年使用:0次
名校
解题方法
5 . 在△ABC中,
.
(1)求![](https://staticzujuan.xkw.com/quesimg/Upload/formula/575212f03d6cd6a84ddcf1c4c955324e.png)
(2)若M为BC上一点,
求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/485688133c06eae9cb558df2f30f8c2a.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/575212f03d6cd6a84ddcf1c4c955324e.png)
(2)若M为BC上一点,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1649b4453e7a76485b8287e0f9bc5072.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82e8ecb371ce77dca5554e8e03b41386.png)
您最近一年使用:0次
名校
解题方法
6 . 如图,在三棱锥
中,
分别是棱
的中点,
,
.
平面
;
(2)求证:
平面
;
(3)求异面直线
与
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c104d1aa4dcec822910d29dd18a8137.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fa7eeef77943d9a8f913ddf27604328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6559aabe16c2318687089e7cc498b98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a65d5853c26657db448af610ac72cca4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b766876252d16f2e331ef2893d45cf04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abd284f76d9f5769bc189508ce2572b.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ce03b310edce42191f9fa75a1c909ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
(3)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
您最近一年使用:0次
名校
解题方法
7 . 在
,
为
边上的中线,点
在
边上,设
.
(1)当
时,求
的值;
(2)若
为
的角平分线,且点
在
边上,求
的值;
(3)在(2)的条件下,若
,求
最小值?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46f744e91051bc298c82461a1b8efbc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764509115979e9958101808383672ec0.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/8a775cd2e88d786d495ae2cb262a2b0f.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/925a74e86290434186f10526e55bd36f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cbce11aa19b8bd2bf6ee5a834e005de.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/82f4f8e27f307a8a998a3335ba7d1bb4.png)
(3)在(2)的条件下,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a655b029decf667584b587052f7b9b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
您最近一年使用:0次
名校
8 . 设,我们常用
来表示不超过
最大整数.如:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d959974d562cb9ef138676ae943bc19c.png)
(2)在锐角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38335830b93ac4d99c28a8e209eecb3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7f5573b30734d65648f61c0a94c98de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6c9bcb51024df4a7d1a04e46ca12549.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c6f4e9bb8b453665bfe9b8fa24711cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26a1633c3dde29b96636a2300ab074f5.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f48da06492a0b0c8a31a5dc1531e8f49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47bb945c963b0d56df9d784d3e3288c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4a9d89ec3d1181091ea159b40952b65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2024高一下·江苏·专题练习
名校
解题方法
9 . 已知
的内角
所对的边分别为
,向量
与
平行.
(1)求
;
(2)若
,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/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f0a69426b756086f177b734275974f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0de8400366e603b83568a0e8a5af9af.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22f9314433f619d6dad2b43f78d39506.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
您最近一年使用:0次
2024-04-15更新
|
2286次组卷
|
16卷引用:重庆市荣昌中学校2023-2024学年高一下学期第二次教学检测(5月)数学试题
重庆市荣昌中学校2023-2024学年高一下学期第二次教学检测(5月)数学试题(已下线)第十一章 解三角形(压轴题专练)-单元速记·巧练(苏教版2019必修第二册)浙江省杭州市富阳区场口中学2023-2024学年高一下学期3月教学质量检测数学试题天津市嘉诚中学2023-2024学年高一下学期第一次月考数学试卷广东省东莞市东莞中学松山湖学校2023-2024学年高一下学期第一次段考数学试题吉林省长春市实验中学2023-2024学年高一下学期第一学程(4月)考试数学试题福建省福州外国语学校2023-2024学年高一下学期期中考试数学试卷广东省中山市中山纪念中学2023-2024学年高一下学期第一次阶段考试数学试题广东省梅州市梅县区丙村中学2023-2024学年高一下学期3月月考数学试卷河南省信阳高级中学2023-2024学年高一下学期5月期中考试数学试题(已下线)专题03 解三角形问题总结-《期末真题分类汇编》(江苏专用)广东省茂名市高州中学2023-2024学年高二下学期3月滚动测试数学试题贵州省遵义市桐梓县荣兴高级中学2023-2024学年高二下学期第一次(3月)月考数学试题(已下线)专题20 三角函数及解三角形解答题(文科)-1(已下线)专题20 三角函数及解三角形解答题(理科)-1湖南省长沙市南雅中学2023-2024学年高二下学期第二次月考(5月)数学试题
名校
10 . 回答下列问题
(1)已知复数
是方程
的根(
是虚数单位,
),求
.
(2)已知复数
,设复数
,(
是
的共轭复数),且复数
所对应的点在第三象限,求实数
的取值范围.
(1)已知复数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c3a38bbc7d2bf07e63e77f1e1945e51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbfb35774829ffc4e5b1f42afadfbad9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a7035cd4adda5d72a9fc9f9fda75995.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec90f93919eb1d1a6b0ed9d05bf91c02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce48af55c99256efdc68fac0767d944c.png)
(2)已知复数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acace49cd87a883accde7d5516dc4f42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79e315ee567d99dc8b8353a943e0fc5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d41042207515dd2e8349c805e6aee400.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af68f652b4c13657ffddf3c9e7eb262b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2024-04-07更新
|
703次组卷
|
4卷引用:重庆市荣昌中学校2023-2024学年高一下学期4月期中考试数学试题
重庆市荣昌中学校2023-2024学年高一下学期4月期中考试数学试题广西南宁市第三十三中学2023-2024学年高一下学期3月月考数学试卷山西省大同市第一中学校2023-2024学年高一下学期4月期中考试数学试题(已下线)10.2 复数的运算-【帮课堂】(人教B版2019必修第四册)