题目内容
若π≤x≤![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024191350253309616/SYS201310241913502533096002_ST/0.png)
【答案】分析:根据2sinx+1=0,得sinx=-
.结合sin
=
和诱导公式sin(π+α)=-sinα,可得x的值.
解答:解:∵2sinx+1=0,∴sinx=-![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024191350253309616/SYS201310241913502533096002_DA/3.png)
∵π≤x≤
,
∴x=π+
=![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024191350253309616/SYS201310241913502533096002_DA/6.png)
故答案为:![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024191350253309616/SYS201310241913502533096002_DA/7.png)
点评:本题给出角的范围和角的正弦值,求角的大小,着重考查了诱导公式和特殊角的三角函数值等知识,属于基础题.
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024191350253309616/SYS201310241913502533096002_DA/0.png)
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024191350253309616/SYS201310241913502533096002_DA/1.png)
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024191350253309616/SYS201310241913502533096002_DA/2.png)
解答:解:∵2sinx+1=0,∴sinx=-
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024191350253309616/SYS201310241913502533096002_DA/3.png)
∵π≤x≤
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024191350253309616/SYS201310241913502533096002_DA/4.png)
∴x=π+
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024191350253309616/SYS201310241913502533096002_DA/5.png)
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024191350253309616/SYS201310241913502533096002_DA/6.png)
故答案为:
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024191350253309616/SYS201310241913502533096002_DA/7.png)
点评:本题给出角的范围和角的正弦值,求角的大小,着重考查了诱导公式和特殊角的三角函数值等知识,属于基础题.
![](http://thumb.zyjl.cn/images/loading.gif)
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