The unit circle shows you all the angles from 0° to 360°. You can also refer to angles as segments of the unit circle circumference from 0 to 2π radians. If you imagine sweeping angles around the unit circle like a radar screen, it makes a series of triangles. The hypotenuse is (depending on how you look at it) either the longest side in the triangle or the radius of the unit circle.

A sine wave is what you get if you plot the triangle’s opposite side versus the angle. Sine waves are important in science and engineering, but also in music. When you’re playing a guitar the frets are all placed where they are to make certain sine waves. Light is a sine wave. Waves are sine waves. The motions of springs are sine waves. It goes on and on!