Here's another way to look at it. If you take any point (x,y) on the unit circle, x is the cosine of the angle made by the line from the origin to (x,y) and the positive x-axis. And y is the sine.

So if you walk around the unit circle holding one of a string, the other end of which is tethered to the origin, the string will make an angle of theta radians with the positive x-axis. Then the coordinates (x,y) are actually (cos theta, sin theta).

From this you can recover SOHCATOA and the standard identities.