已知函数f(x)=sin(x)sin(x+π/2)-√3cos²(3π+x)+1/2√3(x∈R)求f(x)的最小正周期?

问题描述:

已知函数f(x)=sin(x)sin(x+π/2)-√3cos²(3π+x)+1/2√3(x∈R)求f(x)的最小正周期?

f(x)=sin(x)sin(x+π/2)-√3cos²(3π+x)+1/2√3=sinxcosx-√3cos²x+√3/2=(1/2)sin2x-(√3/2)(2cos²x-1)=(1/2)sin2x-(√3/2)cos2x=sin(2x-π/3)所以最小正周期T=2π/2=π