Calculating PhiG: Understanding the Phase Difference Between Waves at w=1

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Tekneek
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Given w =1, What is phiG ? Is it the phase difference between the two waves? If it is, isn't it simply phiG = (delta t/T)*360 but I am not getting the right answer.

PhiG = (0.5/2pi)*360 = 28.6

Also I don't know where this wt + phi = 2pi equation comes from.
 
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The period appears to be about 6.3 s

The diagram is drawn wierdly. The waveforms appear to have a fixed phase difference everywhere except near t = 0 where one has been deliberately distorted to force it through the point (0,0). That origin region would be best ignored, it is so wrong.

There is also a +/- sign associated with the phase difference, according to whether the system introduces a lead or lag, respectively.

I think you should do a google search on: period and phase delay of sinewave
as mastery of this fundamental material is crucial.