Question

已知函数f（x）=sinx+√3cosx

（1）求f（x）最小正周期（2）f（x）单调递减区间f（x）在一区间图像

Answer 1

（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

Answer 2

f(x)=sinx+√3cosx=2*sin(x+π/3)
1. T=2π
2
单调减区间：【2π/3，5π/6】

Answer 3

（1）2π （2）单减区间（2kπ+π/6,2kπ+4π/3）