1 . 某同学用“五点法”画函数
在某一个周期内的图象时,列表并填入了部分数据,如下表:
(1)请在答题卷上将上表
处的数据补充完整,并直接写出函数
的解析式;
(2)设
,求函数
的值域;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e221ad8f28f138eac3d428051da7ace7.png)
![]() | 0 | ![]() | ![]() | ![]() | ![]() |
![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
![]() | 0 | 1 | ![]() | ![]() | 0 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7ec4b4a628ce4482e16a3edc2953fc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f44c3a3d28b1cb09b6c49102a21d7534.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
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2 . (1)在用“五点法”作出函数
的大致图象的过程中,第一步需要将五个关键点列表,请完成下表:
(2)设实数
且
,求证:
;(可以使用公式:
)
(3)证明:等式
对任意实数
恒成立的充要条件是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/467a953b54798b6e2dcd6d76f8817938.png)
0 | |||||
0 | |||||
1 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d95727eed094e7ceb6663ee9d39bda3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/141ba74bc522b95958aea59cdc8c93d0.png)
(3)证明:等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c83576aaf57c7ebdcf56110fdbb0c12a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1d8ae1706a9ea5df3eca17eaa5c8b71.png)
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2024高一下·上海·专题练习
3 . 用“五点法”作出下列函数的简图.
(1)
,
;
(2)
,
.
(3)
在一个周期(
)内的图像.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b7bd295a7ba444f656f55e74ecf5152.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b604c6522119e77c1cb16b91532a2c1.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0402fa82ec4f876f1303bdbcd1f7a2fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ead191140fc7ad2ffcc7fcf91674cb0.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14cdaf2695d9bcb5525cc2335a99ba6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/361c92bf1b5f0fc05b8eab3e89570ed9.png)
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2024高一下·上海·专题练习
4 . 用“五点法”作出下列函数的简图.
(1)
,
;
(2)
,
.
(3)
,
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f22ad2607b23801f0efff27c478b8018.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3072963d9de45cdb182ad348caaac496.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a02268853360f200f176f7cf4c704aeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ec12ca58c9a0de9c8444d1a524f4070.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0e00e84da804ec508a09ed28af41785.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1e9fc088559b30adaf3b434c1460446.png)
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解题方法
5 . 已知函数
,其中
为三角形的内角且满足
.
(1)求出角
.(用弧度制表示)
(2)利用“五点法”,先完成列表,然后作出函数
,在长度为一个周期的闭区间上的简图.(图中
轴上每格的长度为
轴上每格的长度为1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a57c72db976d0fe2f8edb3cf3db9f47d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0b21fe9afffa5e17e101ce87a9376c5.png)
(1)求出角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
(2)利用“五点法”,先完成列表,然后作出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a57c72db976d0fe2f8edb3cf3db9f47d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/626504634b426b5bd86ae5ca22f9a271.png)
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![]() |
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/16/c603f4fe-efc2-43ba-9141-7ef5c7aa8d8c.png?resizew=233)
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2023-12-14更新
|
523次组卷
|
6卷引用:第七章 三角函数(7大易错与3大拓展)-单元速记·巧练(沪教版2020必修第二册)
(已下线)第七章 三角函数(7大易错与3大拓展)-单元速记·巧练(沪教版2020必修第二册)福建省厦门市杏南中学2023-2024学年高一上学期12月月考数学试题(已下线)5.6 三角函数图像的综合应用(AB分层训练)-【冲刺满分】(已下线)专题05 三角函数3-2024年高一数学寒假作业单元合订本(已下线)专题21三角函数的图象与性质-【倍速学习法】(人教A版2019必修第一册)(已下线)7.3.1正弦函数的性质与图像(2)-同步精品课堂(人教B版2019必修第三册)
6 . 在同一平面直角坐标系内画出正弦函数
和余弦函数
在区间
上的图象,并回答下列问题.
(1)写出满足
的x的值;
(2)写出满足
的x的取值范围;
(3)写出满足
的x的取值范围;
(4)当
时,分别写出满足
,
,
的x值的集合.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2b9643da0c0fea4f099f9a9133d6076.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58c65d71e57e6e7697e2f627dcd58583.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bccd6a6e85bdf500218a3e75b31f3c.png)
(1)写出满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d33248aad4efe7b3e8569208e29e8219.png)
(2)写出满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03deca7ddcd6add46570f28ff872945a.png)
(3)写出满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e795ea5ed3eb006ce10ddd787a37319d.png)
(4)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d33248aad4efe7b3e8569208e29e8219.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03deca7ddcd6add46570f28ff872945a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e795ea5ed3eb006ce10ddd787a37319d.png)
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7 . 已知函数
(其中常数
)的最小正周期为
.
(1)求函数
的表达式;
(2)作出函数
,
的大致图象,并指出其单调递减区间;
(3)将
的图象向左平移
个单位长度得到函数
的图象,若实数
满足
,且
的最小值是
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15069b74e83129c2c908c32fc05cf188.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4456675a5dbe545462a22cef9aca8fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70f5389990c3a0c5373f3bd9fb2454c9.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
(2)作出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27794407a3d82a6746f7e0871051f486.png)
(3)将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ec4b31c8c6e293c1e3c2448e7b072f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92fa64657a9b73b0d5c9ea1319e6d658.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc6abf3f9b0ebcdc47a028c781b7edb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037fb348109dc2063a268b10eb925a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
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8 . 已知
.
(1)若
,求
的单调递增区间;
(2)若
,求
的最大值,并指出相应
的值;
(3)当
时,
的值域;
(4)作出函数
的大致图象.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a94c37192477c716fbcc6d66a2f06b3c.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb48434bdcafb5e084fc0b6396cb9469.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(4)作出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
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9 . 已知函数
,
;
(1)用“五点作图法”画出函数在一个周期内的图像(体现作图过程);
(2)若
的图像关于点
对称,且
,求
的值;
(3)不等式
对任意的
恒成立,求实数
的取值范围;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eed4cbe855cac33fc5c17e3b561422f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
(1)用“五点作图法”画出函数在一个周期内的图像(体现作图过程);
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc2ae5a4c0e26403de012495d5207ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3038a4b8c02b12b821fbd0fd69145900.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d40b0c4fd043d372c463db08659e779.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(3)不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab66dbadf24162e3db57849591073717.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e9c48e36f2c35dd8308029445332aa8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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解题方法
10 . 某同学用“五点法”画函数
在某一周期内的图像时,列表并填入的部分数据如下表:
(1)请写出表格中空格处的值,写出函数
的解析式,并画出函数
的大致图像;
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/4/164c8a95-e9a3-4822-8e56-68c29b749753.png?resizew=126)
(2)将函数
的图像向右平移
个单位,再将所得图像上各点的横坐标缩短到原来的
,纵坐标不变,得到函数
的图像,求
的单调减区间.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/575c9fb9e3fe4cb33d21cb34052090f8.png)
![]() | ![]() | ![]() | ![]() | ||
![]() | 0 | ![]() | ![]() | ![]() | ![]() |
![]() | 0 | 1 | 0 | ![]() | 0 |
![]() | 0 | ![]() | 0 | 0 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/4/164c8a95-e9a3-4822-8e56-68c29b749753.png?resizew=126)
(2)将函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0211da37e92f915e781691296578ba0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbb13c41752688ec8361a81a634f9081.png)
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