∵函數(shù)f(x) 的最小正周期為π,∴
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044428312358.png)
=2
∴f(x)=
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044428499412.png)
sin(2x+
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044428328368.png)
+
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044428421477.png)
)
又f(-x)=f(x),所以f(x)為偶函數(shù),即x=0時,f(x)=
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044428499412.png)
,∴
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044428328368.png)
+
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044428421477.png)
=
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044428577687.png)
(k∈Z)
又|
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044428328368.png)
|〈
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044428390507.png)
,∴
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044428328368.png)
=
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044428421477.png)
∴f(x)=
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044428499412.png)
sin(2x+
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044428328368.png)
+
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044428421477.png)
) =
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044428499412.png)
cos2x,不難知道,y="f(x)" 在(0,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044428390507.png)
)單調(diào)遞減
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