# The Unit Circle

### By JonPaul Lambert and Chris Davidson

### What is the Unit Circle?

The Unit Circle is defined as a circle with a radius of one unit. It can and is used to understand the sines and cosines found in right triangles (Chegg). The Unit circle will always have its center at the origin on the Cartesian coordinate plane. A radian is the measure of an angle based on the intersection with the Unit Circle. We can use the Unit Circle to calculate certain angle measures in the coordinate plane. We do this by using points created from the intersection of angles (in the Unit Circle) and the Unit Circle.

As seen above with the moving picture you can see that as the radius circumnavigates around the circle as the sine wave's corresponding points to the circle's degrees is formed. As you can see the top half of the circle forms the positive arc and the bottom half forms the negative arc. Also the degrees 0, 180, and 360 intersect with the x axis. The degrees 90 and 270 make the sine wave's positive and negative arcs tangent to the y value of 1 and -1.

### When, Where, and Who?

The Unit Circle is widely used throughout mathematics, especially trigonometry to this day. It is not known when, where, and who discovered the Unit Circle, but Pythagoras widely used it throughout his works. Also the Greek, Arabic, and Indian civilizations where known to use this fascinating concept of the Unit Circle.