(1)
f(x)=sinx+√3cosx
=2(1/2sinx+√3/2cosx)
=2sin(x+π/3)
f(x)最小正周期T=2π
(2)
由2kπ+π/2≤x+π/3≤2kπ+3π/2
得:2kπ+2π/3≤x≤2kπ+7π/6,k∈Z
f(x)单调递减区间为[2kπ+π/6,kπ+7π/6],k∈Z
(3)
列表:
x+π/3 0 π/2 π 3π/2 2π
x -π/3 π/6 2π/3 7π/6 5π/3
f(x) 0 2 0 -2 0
f(x)=sinx+√3cosx=2*sin(x+π/3)
1. T=2π
2
单调减区间:【2π/3,5π/6】
(1)2π (2)单减区间(2kπ+π/6,2kπ+4π/3)