题目内容
已知函数
的最小正周期为![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211456723464.png)
(1)求
的值;
(2)若不等式
在![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211456801309.png)
上恒成立,求实数
的取值范围
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232114566761584.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211456723464.png)
(1)求
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211456738280.png)
(2)若不等式
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211456785700.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211456801309.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211456832548.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211456863333.png)
(I)
的最小正周期为
,
,
(Ⅱ)由(Ⅰ)可知
,
当![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211456801309.png)
时,有
若不等式
在![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211456801309.png)
上恒成立,
则有
在![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211456801309.png)
上恒成立,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211457222193.png)
,![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211457986933.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211457222193.png)
.
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232114569262448.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232114569411543.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211456957491.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211456723464.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211457004684.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211457019499.png)
(Ⅱ)由(Ⅰ)可知
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211457082985.png)
当
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211456801309.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211456832548.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232114572061232.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211457222193.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211456785700.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211456801309.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211456832548.png)
则有
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232114573621022.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211456801309.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211456832548.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211457222193.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232114579711011.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211457986933.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211457222193.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211458033477.png)
(1)根据诱导公式对式子降幂,化简转化为
形式,再根据最小正周期确定里面参数
的值.
(2)不等式
恒成立转化为
恒成立,然后求出
在
上的最小值和最大值,令
,解关于m的不等式组即可确定m的取值范围.
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211458049938.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211458064308.png)
(2)不等式
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211456785700.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211458127770.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211458142447.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823211456832548.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232114582051213.png)
![](http://thumb.zyjl.cn/images/loading.gif)
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