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...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.
