1 . 下列四个命题:
①函数
与
的图象相同;
②函数
的最小正周期是
;
③函数
的图象关于直线
对称;
④函数
在区间
上是减函数.
其中正确的命题是__________ (填写所有正确命题的序号)
①函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/234310a1e4580ccf8987f034e13a4c59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75dc6c17948bc3bc11a776ec346d9f9d.png)
②函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec95a180f925a142e2dc39808a483603.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86ebba6ed1add0fe647c0226614b9290.png)
③函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/776c6bf310777afe3422a949d1ec89b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ff420ca0d6e2e7d434a933cf6c5792b.png)
④函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0e723fc808c763c238067e724d94abc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b355f70e175cfb3b1d6ed8ad23841e8e.png)
其中正确的命题是
您最近一年使用:0次
2019-04-29更新
|
790次组卷
|
3卷引用:【市级联考】河南省新乡市2018-2019学年高一下学期期中考试数学试题
2 . 设函数
,给出下列结论:①
的一个周期为
;②
的图象关于直线
对称;③
的一个零点为
;④
在
单调递减,其中正确结论有__________ (填写所有正确结论的编号).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3863c3fb5e87da32e49033fe21b469a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b7ada2abc3fa673d7166a0fb4ec00d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1175d698c392debdd6b90cce9d7ad7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49ad2574ea719c4eaec49773a77e98a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9895bf4192f5c55c16f8270d53c49b13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe386ad25a4c1cce633ed4e129127047.png)
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3 . 下列各组函数中,偶函数且是周期函数的是______
填写序号
①
;②
;③
;④
;⑤
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a301324443eb93b467134a86890dd9ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3162d2c7b650bba3e401ffbb1e13bb45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74e7e79ac17c51c7a4aaf9d59ec9beb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a869a76555f3369728f9005863bdb8eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9214539e367939d3f4676758334411d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/802350a5a2cb15949bcbe9017f07634b.png)
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4 . 已知函数
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/12/e4c4496b-99c7-4faf-b3dd-d5c25b9e8eb6.png?resizew=167)
(1)用五点法画出函数
在
上的大致图像,并写出
的最小正周期;
(2)解不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e45ab455db79a0418572805a5fd68a3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/12/e4c4496b-99c7-4faf-b3dd-d5c25b9e8eb6.png?resizew=167)
(1)用五点法画出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc1da1605e6a3419c36192f39bdb0833.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)解不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fcc71bd2da1877d85269abd79496504.png)
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5 . 求下列函数的周期,并借助信息技术画出下列函数的图象进行检验:
(1)
,
;
(2)
,
;
(3)
,
;
(4)
,
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41861c15bf1f061cede9307b4406d751.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/122e7090f6b926ff86c18057443d9c22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/297d041a243cd48af956b2dc479955ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c08ddc8b8501fa143e06cb5277ecc7ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
您最近一年使用:0次
2020-02-06更新
|
1013次组卷
|
4卷引用:人教A版(2019) 必修第一册 逆袭之路 第五章 5.4 三角函数的图象与性质 5.4.2 正弦函数、余弦函数的性质
解题方法
6 . 一根长
(单位:
)的线,一端固定,另一端悬挂一个小球,小球摆动时,离开平衡位置的位移
(单位:
)与时间
(单位:
)的函数关系是:
,
,(其中
);
![](https://img.xkw.com/dksih/QBM/2017/5/23/1693201439629312/1694062501920768/STEM/eabd2bebda394890a7e0a98303e8f348.png?resizew=159)
(1)当
时,小球离开平衡位置的位移
是多少
?
(2)若
,小球每
能往复摆动多少次?要使小球摆动的周期是
,则线的长度应该调整为多少
?
(3)某同学在观察小球摆动时,用照相机随机记录了小球的位置,他共拍摄了300张照片,并且想估算出大约有多少张照片满足小球离开平衡位置的距离(位移的绝对值)比
时小球离开平衡位置的距离小.为了解决这个问题,他通过分析,将上述函数化简为
,
.请帮他画出
的图像并解决上述问题.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9efa9fbcfb9595e2f031aa691db4564b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5873c01192b7d33b7483f444f90b5b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9efa9fbcfb9595e2f031aa691db4564b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d65502a7ea4d1ce6d6d8c720845c73e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26e30f406c0a13a2f93003c6e40658fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc10654ab56f418078352f2b5be5fd95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e003bd597c40163aab143715726e3d57.png)
![](https://img.xkw.com/dksih/QBM/2017/5/23/1693201439629312/1694062501920768/STEM/eabd2bebda394890a7e0a98303e8f348.png?resizew=159)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aeb9a94e392f6759b18abed89aacc5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5873c01192b7d33b7483f444f90b5b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9efa9fbcfb9595e2f031aa691db4564b.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b65f0ae2fab4da18a11dbf73ca04abb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a9cef3cfbceabc23b7410c4be4e638e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a9cef3cfbceabc23b7410c4be4e638e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9efa9fbcfb9595e2f031aa691db4564b.png)
(3)某同学在观察小球摆动时,用照相机随机记录了小球的位置,他共拍摄了300张照片,并且想估算出大约有多少张照片满足小球离开平衡位置的距离(位移的绝对值)比
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aeb9a94e392f6759b18abed89aacc5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d5acdcd3e7a31dd2b3e35f2c0ec2096.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4f76975b7499e28533a8483c852393f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://img.xkw.com/dksih/QBM/2017/5/23/1693201439629312/1694062501920768/STEM/a5a015648a4d49a2a13b9eb797b14553.png?resizew=225)
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