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I seem to recall when taking college Trigonometry my professor saying that the unit circle and sinusoidal curves were basically a mathematical represention of a slinky in that the unit circle was the view of a slinky head on, so that what you saw in the two dimensional sense was a circle, and that when you looked at the slinky from the side (non-compressed of course) you saw the sinusoidal curve.

It's been a while, but I think he mentioned this to help us make the connection (after we had learned the unit circle) to then graphing the sine and cosine fucntions, and how the graphs/values came directly from the unit circle itself (in other words, we were looking at a different side of the same coin so to speak).

I ask because I am helping a student right now in his trig class, and now that he himself has mastered the unit circle, he is moving into graphing the trig functions (sine and cosine at this point) and I'm looking for any little thing that will help him make these connections as well.

I just don't want to use the slinky analogy if that is in fact not true, so I thought I'd defer to those here who clearly know their math better than I. Thanks

Edit: Here's something I was wanting to show my student in this regard and serves to illustrate what I'm saying

It's been a while, but I think he mentioned this to help us make the connection (after we had learned the unit circle) to then graphing the sine and cosine fucntions, and how the graphs/values came directly from the unit circle itself (in other words, we were looking at a different side of the same coin so to speak).

I ask because I am helping a student right now in his trig class, and now that he himself has mastered the unit circle, he is moving into graphing the trig functions (sine and cosine at this point) and I'm looking for any little thing that will help him make these connections as well.

I just don't want to use the slinky analogy if that is in fact not true, so I thought I'd defer to those here who clearly know their math better than I. Thanks

Edit: Here's something I was wanting to show my student in this regard and serves to illustrate what I'm saying

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