已知函數(shù)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240554353901408.png)
).
(1)求函數(shù)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824055435406447.png)
的最小正周期;
(2)若
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240554354371191.png)
,求
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824055435484540.png)
的值.
(1)π;(2)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824055435530598.png)
.
試題分析:(1)先將函數(shù)化為
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824055435546931.png)
的形式,再由
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824055435562614.png)
求得周期;(2)由
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824055435593694.png)
得到sin
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824055435624739.png)
=
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824055435640369.png)
.由
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824055435655813.png)
得到
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824055435671655.png)
的范圍,欲求
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824055435484540.png)
,可進行拆角
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824055435718809.png)
,利用和差化積公式解得.
試題解析: (1)由f(x)=2
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824055435733344.png)
sin xcos x+2cos
2x-1,得f(x)=
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824055435733344.png)
(2sin xcos x)+(2cos
2x-1)=
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824055435733344.png)
sin 2x+cos 2x=2sin
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824055435796691.png)
,所以函數(shù)f(x)的最小正周期為π.(2)由(1)可知f(x
0)=2sin
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824055435624739.png)
.又因為f(x
0)=
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824055435827380.png)
,所以sin
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824055435624739.png)
=
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824055435640369.png)
.由
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824055435655813.png)
,得
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240554358891109.png)
,從而cos
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824055435624739.png)
=
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240554359361172.png)
.所以cos 2x
0=
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240554359671045.png)
=cos
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824055435624739.png)
cos
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824055436014420.png)
+sin
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824055435624739.png)
sin
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824055436014420.png)
=
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824055435530598.png)
.(12分)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824055435546931.png)
的化簡;2、拆角.
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