Question

已知函数f(x)=2sin(π/6－2x)＋a. ⑴求函数f(x)的最小正周期； ⑵求函数f(x)的单调递减区间；

Answer 1

f(x)=2sin(π/6-2x)+a
=2sin(π-(π/6-2x))+a
=2sin(2x+5π/6)+a
(1) T=2π/2=π
(2) π/2+2kπ<2x+5π/6<3π/2+2kπ
-π/3+2kπ<2x<2π/3+2kπ
-π/6+kπ<x<π/3+kπ
f(x)的单调递减区间：-π/6+kπ<x<π/3+kπ k∈Z