Proof of Periodic Sinusoidal waveforms

[tomh]

Homework Statement

Hi,

Have completely forgotten how to prove that a sinusoidal waveform is periodic and can't seem to find it anywhere. So was hoping someone could here.

I've got the signal x(t)=cos(2t+pi/4)

and am trying to prove it is periodic.

Homework Equations

wt=theta

f(x+k)=f(x)

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

The Attempt at a Solution

I know that it is periodic, but to prove I think I have to prove that x(t)=0

Have tried letting t=-pi/8 but with the phase change of pi/2 to convert it to a sine again it gives me a non zero answer.

Anyone with any help would be greatly appreciated.

 

[tiny-tim]

welcome to pf!

hi tomh! welcome to pf!

(have a pi: π and a theta: θ )

cos(A + 2πn) = cosAcos2πn - sinAsin2πn = cosA

does that help?​