题目内容
已知α是第三象限的角,sinα=﹣
,则
=( )
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824045610391281.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824045610423766.png)
A.﹣![]() | B.![]() | C.2 | D.﹣2 |
D
∵α是第三象限角,
∴2kπ+π<α<2kπ+![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824045610485375.png)
∴kπ+
<
<kπ+![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824045610532365.png)
∴tan
<﹣1
sinα=
整理得3tan2
+10tan
+3=0
求得tan
=﹣3或﹣
(排除)
则
=﹣2
故选D.
∴2kπ+π<α<2kπ+
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824045610485375.png)
∴kπ+
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824045610501304.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824045610516301.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824045610532365.png)
∴tan
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824045610516301.png)
sinα=
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824045610563926.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824045610516301.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824045610516301.png)
求得tan
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824045610516301.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824045610610265.png)
则
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824045610625767.png)
故选D.
![](http://thumb.zyjl.cn/images/loading.gif)
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A.﹣![]() | B.![]() | C.2 | D.﹣2 |