已知函数fx=2cos(1/2x- π/3 ),求单调递减区间

题目

已知函数fx=2cos(1/2x- π/3 ),求单调递减区间

答案

令2kπ≤x/2-π/3≤π+2kπ
π/3+2kπ≤x/2≤π+2kπ+π/3
π/3+2kπ≤x/2≤4π/3+2kπ
2π/3+4kπ≤x≤8π/3+4kπ
所以f(x)的单调递减区间：[2π/3+4kπ,8π/3+4kπ]