Well if you consider drawing periodic functions in two dimensions like: cos(t) = x sin(t) = y you get a circle. Adding extra terms to those functions give

Well if you consider drawing periodic functions in two dimensions like: cos(t) = x sin(t) = y you get a circle. Adding extra terms to those functions gives you the epicycles. But, I agree, its not as intuitive because the extra dimensions get in the way of understanding the basic transform.