Question

下列函数哪些是周期函数?对于周期函数指出其周期.

Answer 1

1.y=sin(x)+cos(x)

=根号2*sin(x+π/4)

是周期函数,周期为2π

2.y=sin^2(x)

=(1-cos2x)/2

是周期函数,周期为2π/2=π

3..y=sin(x)+cos(x/2)

是周期函数,周期为4π

sin(x+4π)+cos((x+4π)/2)

=sin(x)+cos(x/2)