函数y=1/2sin(π/4-2x/3)的单调递增区间是

稍等,马上给你答案y=1/2sin(π/4-2x/3)=-1/2sin(2x/3-π/4)
单减间区间求法
令2kπ-π/2 =< 2x/3-π/4 <= 2kπ+π/2
解得单减间区间为[3kπ-3π/8,3kπ+9π/8]]k属于正整数
类似单增区间求法
令2kπ+π/2 =< 2x/3-π/4 <= 2kπ+3π/2
解得单增间区间为[3kπ+9π/8,3kπ+21π/8]，k属于正整数

第二个画图就可以解决
sin(x+（π/4）)的单调增区间为[2kπ-3π/4 ,2kπ+π/4],加绝对值后单增区间为
[kπ-π/4 ,kπ+π/4】，加负号后单增区间为[kπ+π/4 ,kπ+3π/4],

单减区间同理可得[kπ——π/4 ,kπ+π/4],k属于正整数