题目内容
(本小题满分12分)已知函数
(I)求函数
的最小正周期和值域;(II)记
的内角A、B、C的对边分别是a,b,c,若
求角C的值
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231939458801269.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823193945896464.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823193946021549.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231939460361060.png)
(I)![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823193946052240.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231939460681084.png)
,
的最小正周期为
. 因为
,所以
,所以
值域为
.……5分
(II)由(1)可知,
,
,
,
,
得
且
,
, ![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823193946489202.png)
,
,
.…………12分
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823193946052240.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231939460681084.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823193946177776.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823193946192473.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823193946208400.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823193946224436.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823193946239687.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823193945896464.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823193946270322.png)
(II)由(1)可知,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823193946302958.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823193946317967.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823193946364566.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823193946395823.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823193946411733.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823193946426542.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823193946442680.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823193946458794.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823193946473953.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823193946489202.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823193946520470.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823193946536563.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823193946551577.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823193946567829.png)
此题考查三角函数与解三角形的知识
(1)
,
的最小正周期为
。
因为
,![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823193946645642.png)
(2)由(1)可知:
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823193946723845.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823193946785813.png)
点评:在求角度的时候一定要注意角度的范围。
(1)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231939465821433.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823193946598473.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823193946614395.png)
因为
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823193946629664.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823193946645642.png)
(2)由(1)可知:
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823193946676908.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823193946692987.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823193946707983.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823193946723845.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231939467381310.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823193946770822.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823193946785813.png)
点评:在求角度的时候一定要注意角度的范围。
![](http://thumb.zyjl.cn/images/loading.gif)
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