Sine Wave's Fundamental Relationship to the Circle

I've spoken about the sine wave motion's relation to a bigger principle, which I refered to as the wave principle or circle principle before (see here). My admonition was that the "sine wave motion is an icon, i.e. a simplification, of the [circle] principle."

I recently found this illustration on Wikipedia, which depicts the "sine wave's fundamental relationship to the circle" and thought it would be good to post it here as well. The reason I believe it important is because people often become obsessed with the sine wave motion in Taekwon-Do, but do not realise the greater principle (i.e. the "circle principle") it is based on.

What's the point? Basically, the point is that "sine wave" in Taekwon-Do is more than just "bobbing" down-up-down when stepping. In fact, if your concept of the sine wave motion is limited only to stepping or sitting stance punching, you are clearly not understanding the underlying principle. The fundamental principle, of which the sine wave motion is one manifestation, permeates through all our movements. It is part of how we step, true, but it also involves how we chamber, what we do with our hands, how we block, why we rotate our arms when punching, why our techniques start with a "backward motion"; it is even part of our approach to joint-locks and throws. To properly understand the sine wave motion (or any other fundamental way of movement in Taekwon-Do), one has to understand this underlying principle that I call the wave principle, which can just as satisfactory be called the circle principle or Taegeuk ("yin-yang") principle.