f(x)=cos^2x+√3/2sin2x,求函数f(x)的最小正周期及单调递增区间,

f(x)=cos^2x+√3/2sin2x,求函数f(x)的最小正周期及单调递增区间,
f(x)=cos^2x+√3/2sin2x,求函数f(x)的最小正周期及单调递增区间,

f(x)=cos^2x+√3/2sin2x,求函数f(x)的最小正周期及单调递增区间,
f(x)=cos^2x+√3/2sin2x,
=(1+cos2x)/2+√3/2 sin2x
=(√3/2)sin2x+(1/2)cos2x+1/2
=sin2x*cos(π/6)+cos2x*sin(π/6)+1/2
=sin(2x+π/6)+1/2
(1)最小正周期为T=2π/2=π
(2) 增区间
2kπ-π/2≤2x+π/6≤2kπ+π/2
2kπ-2π/3≤2x≤2kπ+π/3
kπ-π/3≤x≤kπ+π/6
即增区间为【 kπ-π/3,kπ+π/6】,k∈Z