题目内容
(本小题满分12分)已知![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225639672289.png)
,![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225639719297.png)
,设函数![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225639781513.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225639672289.png)
.
(Ⅰ)求函数
的最小正周期;
(Ⅱ)求函数
的单调递增区间.
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225639672289.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225639703703.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225639719297.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232256397341055.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225639781513.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225639672289.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225640000301.png)
(Ⅰ)求函数
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225640031495.png)
(Ⅱ)求函数
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225640031495.png)
(Ⅰ)函数
的最小正周期
;
(Ⅱ)单调递增区间为
.
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225640031495.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225640171624.png)
(Ⅱ)单调递增区间为
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232256401871021.png)
先根据数量积的坐标表示及三角恒等变换公式可求出![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225639781513.png)
,易确定其周期,及单调递增区间.
解:(Ⅰ)![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225639781513.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225639672289.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225640000301.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225640327991.png)
=
, 5分
∴函数
的最小正周期
7分
(Ⅱ)由
9分
得![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232256409041065.png)
所以函数
在
上的单调递增区间为
. 12分
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225639781513.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232256402341023.png)
解:(Ⅰ)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225639781513.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225639672289.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225640000301.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225640327991.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232256404521257.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232256402341023.png)
∴函数
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225640031495.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225640171624.png)
(Ⅱ)由
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232256407331199.png)
得
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232256409041065.png)
所以函数
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225640031495.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225641060293.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408232256401871021.png)
![](http://thumb.zyjl.cn/images/loading.gif)
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