题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20190830/20190830001256-20296.png)
(1)求f(x)的最小正周期;
(2)若函数y=f(x)的图象按
![](http://img.shitiku.com.cn/uploads/allimg/20190830/20190830001256-68403.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190830/20190830001257-59059.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190830/20190830001257-71755.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190830/20190830001257-59059.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20190830/20190830001257-16757.png)
解析
试题分析:(1)先利用诱导公式,二倍角公式与和角公式将函数解析式化简整理,然后利用周期公式可求得函数的最小正周期.
(2)由(1)得函数y=f(x),利用函数图象的变换可得函数y=g(x)的解析式,通过探讨角的范围,即可的函数g(x)的最大值.
解:(1)∵f(x)=sinxcosx﹣
![](http://img.shitiku.com.cn/uploads/allimg/20190830/20190830001257-77833.png)
=sinxcosx+
![](http://img.shitiku.com.cn/uploads/allimg/20190830/20190830001257-77833.png)
=
![](http://img.shitiku.com.cn/uploads/allimg/20190830/20190830001257-33317.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190830/20190830001257-71755.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190830/20190830001257-71755.png)
=sin(2x+
![](http://img.shitiku.com.cn/uploads/allimg/20190830/20190830001258-49308.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190830/20190830001258-55357.png)
∴f(x)的最小正周期T=
![](http://img.shitiku.com.cn/uploads/allimg/20190830/20190830001258-11851.png)
(2)∵函数y=f(x)的图象按
![](http://img.shitiku.com.cn/uploads/allimg/20190830/20190830001258-81255.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190830/20190830001259-62065.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190830/20190830001258-55357.png)
∴g(x)=sin(2x+
![](http://img.shitiku.com.cn/uploads/allimg/20190830/20190830001258-49308.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190830/20190830001259-80950.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190830/20190830001259-31953.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190830/20190830001259-31953.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190830/20190830001259-70670.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190830/20190830001300-93241.png)
∵0<x≤
![](http://img.shitiku.com.cn/uploads/allimg/20190830/20190830001300-84004.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190830/20190830001300-83548.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190830/20190830001259-70670.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190830/20190830001300-18350.png)
∴y=g(x)在(0,
![](http://img.shitiku.com.cn/uploads/allimg/20190830/20190830001300-84004.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190830/20190830001257-16757.png)
点评:本题考查了三角函数的周期及其求法,函数图象的变换及三角函数的最值,各公式的熟练应用是解决问题的根本,体现了整体意识,是个中档题.
核心考点
试题【设函数f(x)=sinxcosx﹣cos(x+π)cosx,(x∈R)(1)求f(x)的最小正周期;(2)若函数y=f(x)的图象按=(,)平移后得到的函数y=】;主要考察你对正弦函数的图象与性质等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20190830/20190830001246-52488.png)
A.2-![]() | B.0 | C.-1 | D.-1-![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20190830/20190830001225-50587.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190830/20190830001226-97518.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190830/20190830001226-98737.png)
A.ω=6,φ=![]() | B.ω=6,φ=-![]() |
C.ω=3,φ=![]() | D.ω=3,φ=-![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20190830/20190830001222-30463.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20190830/20190830001219-69491.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190830/20190830001219-28856.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190830/20190830001219-69491.png)
A.f(x)=sin(![]() ![]() | B.f(x)=sin(2x-![]() |
C.f(x)=cos(2x+![]() | D.f(x)=cos(2x-![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20190830/20190830001215-63643.png)
A.2 | B.![]() | C.3 | D.![]() |
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