A Mathematical Trick:

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GeorgeB said:
and as twice the frequency ...

The 1/8 circle comments ... sin (45) = cos (45) = (sqrt(2))/2 = approx 0.707.

45 degrees is 1/8 of a circle.
I think we sometimes forget that cos(ωt) isn't just a triginometric function, but rather a circular triginometric function when discussing standard AC voltage and current. Hence...

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