判断下列函数是否是周期函数,若是,求出其周期?sin(1-2x)sin²x3-Isin4xIxcosx2cos(x/2)-3sin(x/3)

Question

判断下列函数是否是周期函数,若是,求出其周期?
sin(1-2x)
sin²x
3-Isin4xI
xcosx
2cos(x/2)-3sin(x/3)

Answer 1

sin(1-2x)=-sin(2x-1) ,是,周期T=2π/2=π
sin²x =(1-cos2x)/2,是,周期T=2π/2=π
3-Isin4xI ,是,周期T=2π/(4×2)=π/4
xcosx ,不是
2cos(x/2)-3sin(x/3),是是,周期T=12π