Drag the red circle, which is the terminal point for the arc of length on the unit circle. Here are some things to observe.

and are the and coordinates of the terminal point of .

The segment of the tangent line to the unit circle at the terminal point of between the -axis and -axis is of length . The segment also intersects the -axis at and the -axis at .

Notice that very close to , , and become indistinguishable.

By observing similar triangles and with a little algebra, you should be able to determine why , , , and .

You should notice right triangles that show the Pythagorean identities , and . There are other too. See if you can find and prove them.