满足sin(x-π/4)大于等于1/2的x的集合

题目

满足sin(x-π/4)大于等于1/2的x的集合
1/2=sin(π/6)=sin(2kπ+π/6)
1/2=sin(5π/6)=sin(2kπ+5π/6)
sin(x-π/4)>=1/2则2kπ+π/6<=x-π/4<=2kπ+5π/6
所以2kπ+5π/12<=x<=2kπ+13π/12
怎么求出来的sin(x-π/4)>=1/2则2kπ+π/6<=x-π/4<=2kπ+5π/6?

答案

利用y=sinx的图像,发现：若sinx≥1/2,则：2kπ＋π/6≤x≤2kπ＋5π/6,则本题就有：
2kπ＋π/6≤x－π/4≤2kπ＋5π/6