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://thumb.1010pic.com/pic2/upload/papers/20140824/20140824051926048365.png)
cos(x+π)cosx
=sinxcosx+
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824051926048365.png)
cosxcosx
=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824051926079228.png)
sin2x+
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824051926001407.png)
cos2x+
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824051926001407.png)
=sin(2x+
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824051926126250.png)
)+
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824051926141407.png)
∴f(x)的最小正周期T=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824051926188281.png)
=π
(2)∵函数y=f(x)的图象按
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824051926188258.png)
=(
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824051926219252.png)
,
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824051926141407.png)
)平移后得到的函数y=g(x)的图象,
∴g(x)=sin(2x+
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824051926126250.png)
﹣
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824051926266253.png)
)+
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824051926282407.png)
+
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824051926282407.png)
=sin(2x﹣
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824051926313254.png)
)+
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824051926329365.png)
∵0<x≤
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824051926360252.png)
∴
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824051926375284.png)
<2x﹣
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824051926313254.png)
≤
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824051926407250.png)
,
∴y=g(x)在(0,
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824051926360252.png)
]上的最大值为:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824051926032448.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.