【答案】
分析:先根據三角函數的誘導公式將自變量x的系數變?yōu)檎龜�,再由函數y=sin(2x-
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024190840168109402/SYS201310241908401681094003_DA/0.png)
)的單調遞減區(qū)間y=sin(
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024190840168109402/SYS201310241908401681094003_DA/1.png)
-2x)的單調遞增區(qū)間根據正弦函數的單調性求出x的范圍,得到答案.
解答:解:y=sin(
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024190840168109402/SYS201310241908401681094003_DA/2.png)
-2x)=-sin(2x-
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024190840168109402/SYS201310241908401681094003_DA/3.png)
);
∵函數y=sin(2x-
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024190840168109402/SYS201310241908401681094003_DA/4.png)
)的單調遞減區(qū)間y=sin(
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024190840168109402/SYS201310241908401681094003_DA/5.png)
-2x)的單調遞增區(qū)間;
∴2kπ+
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024190840168109402/SYS201310241908401681094003_DA/6.png)
≤2x-
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024190840168109402/SYS201310241908401681094003_DA/7.png)
≤2kπ+
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024190840168109402/SYS201310241908401681094003_DA/8.png)
⇒kπ+
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024190840168109402/SYS201310241908401681094003_DA/9.png)
≤x≤kπ+
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024190840168109402/SYS201310241908401681094003_DA/10.png)
,k∈Z.
∴函數
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024190840168109402/SYS201310241908401681094003_DA/11.png)
的單調增區(qū)間是:[kπ+
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024190840168109402/SYS201310241908401681094003_DA/12.png)
,kπ+
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024190840168109402/SYS201310241908401681094003_DA/13.png)
],k∈Z.
故答案為:[kπ+
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024190840168109402/SYS201310241908401681094003_DA/14.png)
,kπ+
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024190840168109402/SYS201310241908401681094003_DA/15.png)
],k∈Z.
點評:本題主要考查正弦函數的單調性.求正弦函數的單調區(qū)間時先將自變量x的系數根據誘導公式化為正數,再由正弦函數的單調性進行解題.