已知函数f(x)=sinx+√3cosx

2025-01-12 15:19:04
推荐回答(3个)
回答(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

回答(2):

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

回答(3):

(1)2π (2)单减区间(2kπ+π/6,2kπ+4π/3)