题目内容
已知函数![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240108230361379.png)
(1)当
时,求函数
的最小值和最大值;
(2)设
的内角
的对应边分别为
,且
,若向量
与向量
共线,求
的值.
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240108230361379.png)
(1)当
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824010823051806.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824010823067478.png)
(2)设
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824010823098547.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824010823114528.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824010823129464.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824010823145746.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824010823161728.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824010823176705.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824010823192411.png)
(I)
的最小值是
,最大值是
.(II)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824010823067478.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824010823223501.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824010823239266.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824010823254535.png)
试题分析:(I)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240108232701022.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824010823285758.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824010823301857.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824010823317197.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240108233321094.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240108233481157.png)
则
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824010823067478.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824010823223501.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824010823239266.png)
(II)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240108234101120.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824010823426808.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824010823441814.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824010823457812.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824010823473660.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824010823488421.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824010823504546.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824010823519235.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824010823161728.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824010823176705.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824010823566195.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824010823582705.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824010823582515.png)
由余弦定理得,
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240108235971048.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824010823613629.png)
由①②解得
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824010823254535.png)
点评:典型题,本题首先从平面向量的坐标运算入手,得到三角函数式,为研究三角函数的图象和性质,由利用三角函数和差倍半公式等,将函数“化一”,这是常考题型。首先运用“三角公式”进行化简,为进一步解题奠定了基础。涉及三角形中的问题,灵活运用正弦定理、余弦定理,同时要特别注意角的范围。
![](http://thumb.zyjl.cn/images/loading.gif)
练习册系列答案
相关题目