Question

已知函数f(x)=sin^2wx+根号3sinwxsin(wx+π/2)的最小正周期为π,？

Answer 1

f(x)=sin^2wx+√3sinwxsin(wx+π/2)
=sin^2wx+√3sinwxcoswx
=1/2(1-cos2wx)+√3/2sin2wx
=√3/2sin2wx-1/2cos2wx+1/2
=sin(2wx-π/6)+1/2
∵f(x)最小正周期T=π
∴2π/(2w)=π,w=1
f(x)=sin(2x-π/6)+1/2
∵x∈(-π/12,π/2)
∴2x∈(-π/6,π)
2x-π/6∈(-π/3,5π/6)
∴-√3/2,9,已知函数f(x)=sin^2wx+根号3sinwxsin(wx+π/2)的最小正周期为π,
当x∈（-12分之π,2分之π）时,求函数f（x）的值域