题目内容
已知复数
,
,且
.
(1)若
且
,求
的值;
(2)设
=
,求
的最小正周期和单调减区间.
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823134620014492.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823134620030884.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823134620061228.gif)
(1)若
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823134620077245.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823134620092297.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823134620124187.gif)
(2)设
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823134620233197.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823134620233270.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823134620233270.gif)
(1)![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823134620326536.gif)
(2)函数的最小正周期为
-;
的单调减区间![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823134620451825.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823134620326536.gif)
(2)函数的最小正周期为
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823134620420241.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823134620233270.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823134620451825.gif)
(1)∵![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823134620061228.gif)
∴
∴![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/2014082313462049873.gif)
-------------2分
若
则
得
----------------------------4分
∵
∴
或![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823134620966447.gif)
∴
-------------------------------------------------6分
(2)∵![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231346210131260.gif)
=![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823134621044848.gif)
--------------9分
∴函数的最小正周期为
-----------------------------------------10分
由
得![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823134621106855.gif)
∴
的单调减区间
.-------------------------12分
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823134620061228.gif)
∴
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823134620482824.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/2014082313462049873.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823134620529622.gif)
若
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823134620077245.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823134620560626.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823134620623479.gif)
∵
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823134620810306.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823134620935450.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823134620950417.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823134620966447.gif)
∴
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823134620326536.gif)
(2)∵
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231346210131260.gif)
=
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823134621044848.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823134621060573.gif)
∴函数的最小正周期为
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823134620420241.gif)
由
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823134621091879.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823134621106855.gif)
∴
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823134620233270.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823134620451825.gif)
![](http://thumb.zyjl.cn/images/loading.gif)
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