名校
解题方法
1 . 现定义“
维形态复数
”:
,其中
为虚数单位,
,
.
(1)当
时,证明:“2维形态复数”与“1维形态复数”之间存在平方关系;
(2)若“2维形态复数”与“3维形态复数”相等,求
的值;
(3)若正整数
,
,满足
,
,证明:存在有理数
,使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9dc4e868a310c371ff88075d8a966a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef9d830212489b316bb052455098108e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a7035cd4adda5d72a9fc9f9fda75995.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edc8299790d98621b87e73212a2ebb91.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/905dd10639c9fef5ef8d66a124756140.png)
(2)若“2维形态复数”与“3维形态复数”相等,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c136aaf9b5dedec254a92ce302f4a70c.png)
(3)若正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94742ebbb028c50d7a58e3e8f4ab329c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35490c12e57ecd91af9934cb17b5c927.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ed110fbfeb14003270a1039ba174d0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f02f2606180ffeda602ff9ae747af6f.png)
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2024-05-11更新
|
709次组卷
|
3卷引用:安徽省合肥市第一中学2023-2024学年高一下学期5月期中联考数学试题
解题方法
2 . 已知数列
满足
.
(1)求数列
的通项公式;
(2)若数列
满足
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26240108bc9013a4e17a8cdc197742e9.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff69ee18a3dfbc55f9a1dad39573d4ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/064602515e65e80eb8e528411ea3f594.png)
您最近一年使用:0次
名校
3 . 设
,函数
,
.
(1)讨论函数
的零点个数;
(2)若函数
有两个零点
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1f9f547dfe47595966f30b27c2f59fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e5c9dd749202f50f605cc804bedbe1f.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e493961c69910188bf8fd9fd04e27f0.png)
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名校
解题方法
4 . 对于角的集合
和角
,定义
为集合
相对角
的“余弦方差”.
(1)集合
和
相对角
的“余弦方差”分别为多少?
(2)角
,集合
,求
相对角
的“余弦方差”为多少?
(3)角
,集合
,求
相对角
的“余弦方差”是否有最大值?若有求出最大值,若没有说明理由?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94201a1fe57d13f172c3347fe2f2f0c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0578330c7c71ecdf4354d855174051a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94201a1fe57d13f172c3347fe2f2f0c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
(1)集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1894b46e13b35c59a8868c301df8c4c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eae35267fd999a81a65596312be5bf31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
(2)角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1676b17f3641daf630f709517d22d120.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97e2bf1f8cf438ad7898cf463b2ab07e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
(3)角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1b18694da971f8a3bf64ca54b4d5198.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/740d1fc2346ac825c16515558b1af667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
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5 . 由两角和差公式我们得到倍角公式
,实际上
也可以表示为
的三次多项式.
(1)试用
表示
.
(2)求
的值;
(3)已知方程
在
上有三个根,记为
,
,
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b327b904e4d65a88b5adaf4de91694fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e711ddf15e0ebc5562b9f7314d199a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45b8b77522dfc890b99f0a86a690de94.png)
(1)试用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45b8b77522dfc890b99f0a86a690de94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e711ddf15e0ebc5562b9f7314d199a.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/460dc20cc2eb8beb9eac71c5b00b4a7b.png)
(3)已知方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b322f4b08de183d0897d4d81050d9e63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/455ba3d3e46977fcbe5b71f8bb9df4be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291c25fc6a69d6d0ccfb8d839b9b4462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de69d39442b502967d587ae85c60f4e8.png)
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名校
解题方法
6 . 筒车是我国古代发明的一种水利灌溉工具,因其经济又环保,所以至今还在农业生产中被使用.如图,假定在水流稳定的情况下,一个直径为10米的筒车开启后按逆时针方向匀速旋转,转一周需要1分钟,筒车的轴心O距离水面的高度为
米.以盛水筒P刚浮出水面时开始计算时间,设筒车开始旋转t秒后盛水筒P到水面的距离为h米(规定:若盛水筒P在水面下,则h为负数).
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/17/6368d96c-e8a8-45e1-8142-df1bb0558cc2.png?resizew=199)
(1)写出h(单位:米)关于t(单位:秒)的函数解析式
(其中
,
,
);
(2)若盛水筒P在
,
时刻距离水面的高度相等,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/533a7b702ada1dd80123e4041271d521.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/17/6368d96c-e8a8-45e1-8142-df1bb0558cc2.png?resizew=199)
(1)写出h(单位:米)关于t(单位:秒)的函数解析式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cecdd962e61da34c1312c1da537d9a7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13378be06b6b01bcad1d261ff14e87cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4456675a5dbe545462a22cef9aca8fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7c9e46448bc791c441ca02d8f4508eb.png)
(2)若盛水筒P在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c7eb49a823f757461cd5260757b088.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cd84a8f95166367063218ee03ffd5a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd43409a358dca98d58b8dcc28d84e50.png)
您最近一年使用:0次
2023-02-16更新
|
1482次组卷
|
10卷引用:陕西省榆林市2022-2023学年高一上学期期末数学试题
陕西省榆林市2022-2023学年高一上学期期末数学试题江西省南昌市江西科技学院附属中学2022-2023学年高一下学期3月月考数学试题河南省新乡市卫辉市第一中学等2校2022-2023学年高一上学期期末数学试题(已下线)第五章 三角函数(压轴题专练)-速记·巧练(人教A版2019必修第一册)浙江省湖州市长兴县雉城中学2023-2024学年高一上学期期末数学复习卷一(已下线)高一上学期期末复习【第五章 三角函数】(拔尖篇)-举一反三系列(已下线)高一上学期期末考试解答题压轴题50题专练-举一反三系列(已下线)第五章 三角函数单元测试(基础版)-【冲刺满分】河南省安阳市林州市第一中学2023-2024学年高一下学期3月检测一数学试题江西省宜春中学2023-2024学年高一下学期(基础部)第一次月考数学试卷
7 . 化简:
(1)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/073496d29115ad184dd56514183371e4.png)
;
(2)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbb9700dd1f9d9a729f3e1a1559fe314.png)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/073496d29115ad184dd56514183371e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f51bf4a1a148de0d86fb99915ac4c5e1.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbb9700dd1f9d9a729f3e1a1559fe314.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdd0ec23e454440796739087fde0a373.png)
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2022-08-19更新
|
2823次组卷
|
10卷引用:苏教版(2019) 必修第二册 过关斩将 第10章 10.3 几个三角恒等式
苏教版(2019) 必修第二册 过关斩将 第10章 10.3 几个三角恒等式(已下线)专题06 三角函数(讲义)-2(已下线)专题2三角求值运算 (提升版)(已下线)专题05 几个三角恒等式-期中期末考点大串讲(苏教版2019必修第二册)(已下线)第四章 三角函数与解三角形 第三节 三角恒等变换 第一课时 两角和、差公式和倍角公式(B素养提升卷)(已下线)模块二 专题5《三角恒等变换》单元检测篇 A基础卷 (人教A)期末终极研习室(已下线)专题10 几个三角恒等式-【寒假自学课】(苏教版2019)(已下线)考点11 倍(半)角公式及其应用 --2024届高考数学考点总动员【练】(已下线)FHsx1225yl056(已下线)模块一专题5《三角恒等变换》单元检测篇A基础卷(人教B)
名校
8 . 对于定义域为
的函数
,若存在实数
使得
对任意
恒成立,则称函数
具有
性质.
(1)判断函数
与
是否具有
性质,若具有
性质,请写出一个
的值,若不具有
性质,请说明理由;
(2)若函数
具有
性质,且当
时,
,解不等式
;
(3)已知函数
,对任意
,
恒成立,若由“
具有
性质”能推出“
恒等于
”,求正整数
的取值的集合.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/608ceff5d48b2a65a48910152750ba68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fbde2170c24819edd47db617810bf47.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a04e15196ce905f578e53b845242ee30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b6da64d1686393e0ec9d4c6acfcf86e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fbde2170c24819edd47db617810bf47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fbde2170c24819edd47db617810bf47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fbde2170c24819edd47db617810bf47.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a5d8bc28ee110a9540f383828b7d245.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790daaa89fc9d093f45023becf765697.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbea50b9ee9088ba9c3b474a893fc52b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18ae489dfcc8fd3862b57feffa168d2e.png)
(3)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dac47c1b6230edf33b5a1c76b75025de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26c6e90b4ae31c5471829c269cc0d789.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
2022-06-25更新
|
692次组卷
|
4卷引用:上海市闵行区2022届高考二模数学试题
名校
解题方法
9 . 已知函数
在区间
(
)上的最大值为
,最小值为
,记
.
(1)求
的值;
(2)设
(
).
①若
,试写出方程
的一个解;
②若
,求函数
的零点个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4cf09da768a659c25700eeb0fd08c46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d506b5bc2b8ca74deb11ffe51aaa5e12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bf039c46a25e331446c6ee1e9af3c82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5dc99a0493caf8b65827518c965e8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b075efa175a26b8deae739f1bd7cab52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a21103513520dc13e50c353ac98234d3.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5bbe8f9526a8b16f730e8a45064fe5d.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af0fad3e5959a6137d2b830ca0babede.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/698eb513eca33513eaffec96b7a9871b.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87486f1fa51d9de597928723162a89ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0225bca34eaf19544939b29153aac1.png)
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2022-06-19更新
|
1102次组卷
|
3卷引用:湖南省长沙市第一中学2021-2022学年高一下学期第三次阶段性检测数学试题
10 . 已知函数
, 若存在实数
, 使得对于定义域内的任意实数
,均有
成立, 则称函数
为 “可平衡” 函数, 有序数对
称为函数
的 “平衡” 数对;
(1)若
, 求函数
的 “平衡” 数对;
(2)若
, 判断
是否为 “可平衡” 函数, 并说明理由;
(3)若
, 且
均为函数
的 “平衡” 数对, 求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db40d5295942e85ec07a3728c7ad308d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b35c9f4a622bfa1c0ac47e3e4743070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c996b4493eeffa33e4606dc8457c0ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f6bfdb24ecf5da863405c2b40936ff9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed8f7e2a6d5a7c94c41687c21afb48c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f6bfdb24ecf5da863405c2b40936ff9.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/560e9ae1410234c91e018b932684d3d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f6bfdb24ecf5da863405c2b40936ff9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc304a55feec5d8312d3082f1bb91a23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294fe9f85ca15496f9e63b2a8ece70ee.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b719f5d8298f9686861a1c7aaac005b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2cfbf73de206ae31160923e52efa653.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f037d9cba880bcafab3283b2a3e9865c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db0e414b032d05f06c58ae6e95874d10.png)
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