题目内容
已知函数![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232258094661020.png)
(1)求函数
的最小正周期和值域;
(2)若
,且
,求
的值.
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232258094661020.png)
(1)求函数
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225809481463.png)
(2)若
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225809497936.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225809512586.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225809544418.png)
(1)周期为
,值域为
;(2)![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225809731348.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225809637367.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225809700492.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225809731348.png)
(1)通过降幂公式和三角恒等变换公式可得![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225809746746.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225809934844.png)
由此易得函数的周期和值域.
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225809949754.png)
……………3分
函数
的周期为
, 又
故函数
的值域为
…5分
(2) 由
,得
可得![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232258106671132.png)
再根据
求值即可.
∵
,∴
即
……………6分
因为
,所以
,于是
……………8分
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232258108233588.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225809746746.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225809934844.png)
由此易得函数的周期和值域.
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225809949754.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225809934844.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225809996193.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225810058431.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225809637367.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225810339860.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225810058431.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225809700492.png)
(2) 由
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225809512586.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225810495903.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232258106671132.png)
再根据
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232258106821191.png)
∵
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225809512586.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225810495903.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232258106671132.png)
因为
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225810760942.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225810776965.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232258108071627.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232258108233588.png)
![](http://thumb.zyjl.cn/images/loading.gif)
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