解题方法
1 . 在数学史上,为了三角计算的简便并且更加追求计算的精确性,曾经出现过下列两种三角函数:定义
为角
的正矢,记作
;定义
为角
的余矢,记作
.给出下列结论:
①函数
在
上单调递增;
②若
,则
;
③若
,则
的最小值为0;
④若
,则
的最小值为
.
其中所有正确结论的序号为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54b7b2ba487fb7e7063a4f95ea81c94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52e98f5ac7415a262664dd6c2e8eacf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d54bbf533362dbef1dae0345afae92f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42f539be9908400df3c3e679e6b8e0e8.png)
①函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfb58e2e08a817e6279d9116012b0518.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccc08b681e246016cd05802b234760e0.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb245aa9a36dc82042dead26f2de3400.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06895303e65f0a987c429a83ff01235b.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/812e2fd49b011c1af000001dea81ef99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
④若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc78b4b6a74d63b6d76496e80791e49b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb88b6e17cd00140b747b585a6644d39.png)
其中所有正确结论的序号为( )
A.①② | B.③④ | C.①③④ | D.②③④ |
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21-22高三上·北京·期中
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解题方法
2 . 已知函数
,任取
,定义集合
点
满足
.设
分别表示集合
中元素的最大值和最小值,记
,给出以下四个结论:①若函数
,则
;②若函数
,则
的最大值为
;③若函数
,则
在
上单调递增;④若函数
,则
的最小正周期为2,其中所有正确结论的序号为__________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09b29a7faa14a6e09d0db2d04f4ced03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/995ec593baa4ef50b6d87c78380953d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef57fffaa2a73fae4cb219c6ccbf2929.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f71f4ac48908498a5a9eb4d62f5cf27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/676ada988580ff4365da61820eddcef6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3215494dccf60336e9f7740d19fcbc57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50f26d721b107f8b2bc88f3eb0f42c70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77d2bbe03029a32873463dd93998605d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/318a16f1950d06e5500c76d8f81a507f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed05ed8d7e1011a7df20e484ea87325c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/318a16f1950d06e5500c76d8f81a507f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fecc65b2bfb207896ef00c42334caaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfb7201e3e41346c74f49e0687430b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fecc65b2bfb207896ef00c42334caaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/972cfd3677c0f6342a57d3ab58cf0356.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfb7201e3e41346c74f49e0687430b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fecc65b2bfb207896ef00c42334caaf.png)
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4卷引用:江西省永新中学2021-2022学年高二上学期第一次段考数学(理)试题
江西省永新中学2021-2022学年高二上学期第一次段考数学(理)试题北京市第十一中学2023届高三上学期11月月考数学试题(已下线)北京市第四中学2022届高三上学期期中考试数学试题(已下线)专题2.2 模拟卷(2)-2022年高考数学大数据精选模拟卷(新高考地区专用)
3 . 法国数学家费马于1640年提出了猜想:
是质数.这种具有美妙形式的数被称为费马数,因为随着n的增大,
迅速增大,所以要判断费马的猜想是否正确非常不容易,一直到1732年才被数学家欧拉算出
,才证明费马的猜想是错误的.若数列
满足
,则满足
的最小正整数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f3cb8d72bb2e281b943b3b430138ef7.png)
_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b280ca78acd062dd380c5aab0c8a080d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e9da2b0e7b9eca965043be2f38a91f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30ac5abd893e2158c86f56e697f452ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b735f6763180ee636d33b8f3e08af5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59b4e016c5b16331faa6a0e25f3acf58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f3cb8d72bb2e281b943b3b430138ef7.png)
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2卷引用:河北省衡水市第十三中学2022-2023学年高二上学期质检(三)数学试题
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4 . 数学中有许多形状优美、寓意美好的曲线,曲线
就是“心形”曲线.给出以下列两个结论:
①曲线
恰好经过6个整点(即横、纵坐标均为整数的点);
②曲线
上任意一点到原点的距离都不超过
;
则正确的判断是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/6/6fea8eb5-9b2c-4524-a34a-baaf6d03d853.png?resizew=151)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec03995f3d289f47654e71af0affde19.png)
①曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
②曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
则正确的判断是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/6/6fea8eb5-9b2c-4524-a34a-baaf6d03d853.png?resizew=151)
A.①正确②错误 | B.①错误②正确 |
C.①②都错误 | D.①②都正确 |
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