Wrapping the Real Numbers Around the Unit Circle


The Wrapping Function is created by wrapping a number line around the unit circle. Each number on the number line will fall on top of exactly one point on the unit circle. In the graphic below, as you wrap the number line around the circle in the positive direction or negative directions, X1 represents the distance/arc length of the red arc that has been wrapped around the unit circle. The wrapping function, W(X1), then takes in that distance and spits out a point on the unit circle.

What are some notable values of ? ?

What is the relationship between , a unit-less measure of the real line, the arc length along the unit circle, and the central angle ?