函数y=sin(x+π/3)sin(x+π/2)的最小正周期T=?

函数y=sin(x+π/3)sin(x+π/2)的最小正周期T=?
函数y=sin(x+π/3)sin(x+π/2)的最小正周期T=?

函数y=sin(x+π/3)sin(x+π/2)的最小正周期T=?
y=sin(x+π/3)sin(x+π/2)
=sin(x+π/3)cosx
=(sinxcosπ/3+sinπ/3cosx)cosx
=sinxcosx/2+√3/2 cos²x
=sin2x/4+√3/4cos2x+√3/4
=1/2sin(2x+Ф)+√3/4
∴T=2π/2=π
周期是π