Question

函数:y=cos(x-π/3)的单调递减区间是

Answer 1

解答：
y=cosx的单调减区间是[2kπ,2kπ+π]
2kπ≤x-π/3≤2kπ+π
∴
2kπ+π/3≤x≤2kπ+4π/3
即函数:y=cos(x-π/3)的单调递减区间是【2kπ+π/3，2kπ+4π/3】，k∈Z

Answer 2

y'=-2sin(2x-π/3),若函数单调递减,应有
y'=-2sin(2x-π/3)<0,即
sin(2x-π/3)>0,
0<(2x-π/3)<π,
解此不等到式得:π/6则函数y=cos(2x-π/3)的单调递减区间为:
(π/6)+2kπ<x<(2π/3)+2kπ.