题目内容
设函数y=sin(ωx+φ)(ω>0,φ∈(-
,
))的最小正周期为π,且其图象关于直线x=
对称,则在下面四个结论中:①图象关于点(
,0)对称;②图象关于点(
,0)对称;③在[0,
]上是增函数;④在[-
,0]上是增函数,所有正确结论的编号为________.
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824052743361421.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824052743361421.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824052743392455.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824052743408396.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824052743424413.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824052743439420.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824052743439420.png)
②④
∵T=π,∴ω=2.
又2×
+φ=kπ+
,∴φ=kπ+
.
∵φ∈(-
,
),∴φ=
,∴y=sin(2x+
).
由图象及性质可知②④正确.
又2×
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824052743392455.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824052743361421.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824052743424413.png)
∵φ∈(-
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824052743361421.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824052743361421.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824052743424413.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824052743424413.png)
由图象及性质可知②④正确.
![](http://thumb.zyjl.cn/images/loading.gif)
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