You can put this solution on YOUR website! First, radian measure of angles
compared to degree is:
radians --- degrees
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0 ------------ 0
pi/2 --------- 90
pi ----------- 180
3pi/2 -------- 270
2pi ---------- 360, 0
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A definition of period would be:
"What is the shortest span of radians
for which the waveform keeps repeating
itself ?"
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You are correct in saying that the
sin wave keeps repeating itself if
you take -pi to +pi as your sample,
but if you measure the wavelength, You get
the same answer. Any sample of the
wave that is 2pi radians long gives
you a repeating portion.
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Hope this helps