题目内容
若cosx=-
,x∈[0,π],则x的值为( )
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823175829607356.png)
A.arccos![]() | B.π-arccos![]() | C.-arccos![]() | D.π+arccos![]() |
B
本题考查反三角函数的性质
因为
,
,则![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823175829904681.png)
由诱导公式有
,则![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823175829935700.png)
所以![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823175829951702.png)
因为
,且![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823175830107948.png)
所以![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231758301221058.png)
故正确答案为B
则
或![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231758301531095.png)
因为
,而![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231758301851033.png)
因为
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823175829841549.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823175829857521.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823175829904681.png)
由诱导公式有
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823175829919727.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823175829935700.png)
所以
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823175829951702.png)
因为
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823175829857521.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823175830107948.png)
所以
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231758301221058.png)
故正确答案为B
则
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231758301381130.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231758301531095.png)
因为
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823175829857521.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231758301851033.png)
![](http://thumb.zyjl.cn/images/loading.gif)
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A.arccos![]() | B.π-arccos![]() | C.-arccos![]() | D.π+arccos![]() |