名校
解题方法
1 . 任意一个复数z的代数形式都可写成复数三角形式,即
,其中i为虚数单位,
,
.棣莫弗定理由法国数学家棣莫弗(1667~1754)创立.设两个复数用三角函数形式表示为:
,
,则:
.如果令
,则能导出复数乘方公式:
.请用以上知识解决以下问题.
(1)试将
写成三角形式;
(2)试应用复数乘方公式推导三倍角公式:
;
;
(3)计算:
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09a0f4e84ca890b19f1a2d39b9c4d6f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/826ff108f47b7dc4dd2e63e14c204a0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a34f45fe480fe6100c86a13db7ac652f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93d74cc1db74efb3bf74930e0ca3621a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b20d6f11c0a25c45c86eced22ec6405.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1681d16c04032fcc92d7931524106b05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed43030ca376eb5e3331d75f103fc762.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/785e47874ebcab903e4ac95fbd8f30aa.png)
(1)试将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb232df15bbcb2addccf8d5e7adc4d1f.png)
(2)试应用复数乘方公式推导三倍角公式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a47bdf9c678020d1d50082f7bb208557.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1266e4d6e189cbd788785b44eb4491d6.png)
(3)计算:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5b5976d1eab3219c6be0f3e85b4f406.png)
您最近一年使用:0次
2024-06-07更新
|
640次组卷
|
4卷引用:江西省南昌市江西科技师范大学附属中学2023-2024学年高一下学期第二次月考数学试卷
江西省南昌市江西科技师范大学附属中学2023-2024学年高一下学期第二次月考数学试卷江西省南昌市江西科技学院附中2023-2024学年高一下学期5月份月考数学试卷重庆市育才中学校2023-2024学年高一下学期阶段测试数学试题(已下线)10.3 复数的三角形式及其运算-【帮课堂】(人教B版2019必修第四册)
解题方法
2 . 已知锐角
的三个内角
,
,
的对边分别是
,
,
,且
的面积为
.则下列说法正确的是( )
![](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/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2399f71125b424fd17c5da2ae796e5ce.png)
A.![]() |
B.![]() ![]() |
C.若![]() ![]() |
D.若![]() ![]() ![]() |
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2024-06-07更新
|
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4卷引用:江西省南昌市江西科技师范大学附属中学2023-2024学年高一下学期第二次月考数学试卷
名校
解题方法
3 . 双曲线C:
的离心率为
,点
在C上.
(1)求C的方程;
(2)设圆O:
上任意一点P处的切线交C于M、N两点,证明:以MN为直径的圆过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3040b6c904477030ecf8ba20b2b18759.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46529ee9b4550db1c12f187e1fbebde0.png)
(1)求C的方程;
(2)设圆O:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d61985901c2bc698d72ac88f4e1eb65.png)
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2024-06-04更新
|
495次组卷
|
2卷引用:江西省南昌市第十九中学2024届高三下学期第五次模拟考试数学试卷
名校
解题方法
4 . 函数
及其导函数
的定义域均为R,
和
都是奇函数,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e81e15b871dd32b2438ef8025bcc42d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbd86412261efa98cc6bdd1b4c1cd00e.png)
A.![]() ![]() | B.![]() ![]() |
C.![]() | D.![]() |
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2024-05-29更新
|
699次组卷
|
2卷引用:江西省南昌市第十中学2023-2024学年高三下学期“三模”考试数学试题
名校
解题方法
5 . 设抛物线C:
(
),直线l:
交C于A,B两点.过原点O作l的垂线,交直线
于点M.对任意
,直线AM,AB,BM的斜率成等差数列.
(1)求C的方程;
(2)若直线
,且
与C相切于点N,证明:
的面积不小于
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b35f0b940c8422ef47edc3b7ce55e47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5abd313d4e92a762fb7fb0c1cb65263d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02ebce8b2a915356ed39f36c5bad2ebe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1d0aa9412dd7caf42cc71520e282328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aff8d9b6533ff319420cdc5e8740b04.png)
(1)求C的方程;
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edc05c94ee6367e5551b219ac3168865.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98013a5042685a1db94249e70c62c09a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
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2024-05-26更新
|
2981次组卷
|
5卷引用:江西省南昌市八一中学2024届高三下学期三模测试数学试题
江西省南昌市八一中学2024届高三下学期三模测试数学试题2024届广东省深圳市二模数学试题(已下线)第30题 几何分析曲径通幽,代数推演水到渠成(优质好题一题多解)安徽省六安第一中学2023-2024学年高三下学期期末质量检测卷(二)数学试题(已下线)易错点8 圆锥曲线问题中未讨论直线斜率的特殊情况
名校
解题方法
6 . 已知函数
及其导函数
的定义域均为
,记
.
满足
,
的图象关于直线
对称,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c765461ae1a6c70f5cbdcb6c932a22b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/205b6623a0158130a701284de57bd331.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62c36601834a9a0e473ff9b17cd66458.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2024-05-23更新
|
653次组卷
|
2卷引用:江西省南昌市八一中学2024届高三下学期三模测试数学试题
解题方法
7 . 如图,有一张较大的矩形纸片
分别为AB,CD的中点,点
在
上,
.将矩形按图示方式折叠,使直线AB(被折起的部分)经过P点,记AB上与
点重合的点为
,折痕为
.过点
再折一条与BC平行的折痕
,并与折痕
交于点
,按上述方法多次折叠,
点的轨迹形成曲线
.曲线
在
点处的切线与AB交于点
,则
的面积的最小值为_________________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dcab46b9032d25a660af389a6a37210.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192f4f9446c954a291f779d963f90257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d71ba52c97faad3a085b9989969145.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d36626c9e45a25e8dc5bf4be4dbbfb3.png)
您最近一年使用:0次
2024-05-20更新
|
693次组卷
|
2卷引用:江西省南昌市2024届高三第二次模拟测试数学试题
8 . 如图所示,用一个不平行于圆柱底面的平面,截该圆柱所得的截面为椭圆面,得到的几何体称之为“斜截圆柱”.图一与图二是完全相同的“斜截圆柱”,AB是底面圆
的直径,
,椭圆所在平面垂直于平面ABCD,且与底面所成二面角为
,图一中,点
是椭圆上的动点,点
在底面上的投影为点
,图二中,椭圆上的点
在底面上的投影分别为
,且
均在直径AB的同一侧.
时,求
的长度;
(2)(i)当
时,若图二中,点
将半圆均分成7等份,求
;
(ii)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/526908dfb46cf151b8ab1492a9d52047.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30c20e88a33043f4279fff360c81006e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d1d663b6001346d11600f064cfcb7a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07d26ebb800066a7bce57213cd074005.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07d26ebb800066a7bce57213cd074005.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b20bf4f818b494e7b5fa9c68527026e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/893ff0f9b64c66312c37cb7ce90c351d.png)
(2)(i)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c345907ebe27888332b1b44c666cc47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bde134aa77da12366e6a742fa33b4bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e578d74f75cf5a087cb5dbad1d07c66.png)
(ii)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d0838e80d58bad3e9cbc4766d2a0ec3.png)
您最近一年使用:0次
解题方法
9 . 校足球社团为学校足球比赛设计了一个奖杯,如图,奖杯的设计思路是将侧棱长为6的正三棱锥
的三个侧面沿AB,BC,AC展开得到面
,使得平面
均与平面ABC垂直,再将球
放到上面使得
三个点在球
的表面上,若奖杯的总高度为
,且
,则球
的表面积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66a3857b390b5cd3618625795b0cd4fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66a3857b390b5cd3618625795b0cd4fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f7807638578edd712265463a7a5eab0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ec978eb43bc4f9e7df83b0d0195dcda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
10 . 已知
且
.
(1)当
时,求证:
在
上单调递增;
(2)设
,已知
,有不等式
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89b9e1ee18c04dbe1c9beaf49fa67207.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37fa1476cf3552b9ae91ef039b1c6c80.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0ffecb03c47be920254c4ccffa5b222.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6408a113793f7d7aa6b430d436d711d0.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7db8f867196410e2828e2bbd3183b02d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7c48c1bbf3082d238c355fb0f616622.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22e38c541dec8fce1d26886e5ef7d21f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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