下列函数哪些是周期函数?对于周期函数指出其周期.1.y=sin(x)+cos(x)2.y=sin^2(x)3.y=sin(x)+cos(x/2)

Question

下列函数哪些是周期函数?对于周期函数指出其周期.
1.y=sin(x)+cos(x) 2.y=sin^2(x) 3.y=sin(x)+cos(x/2)

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)