Unit circle

circle with radius one

In mathematics, a unit circle is a circle with a radius of 1. The equation of the unit circle is . The unit circle is centered at the Origin, or coordinates (0,0). It is often used in Trigonometry.

The Unit Circle can be used to model every Trigonometric function.

Trigonometric functions in the unit circle change

In a unit circle, where   is the angle desired,   and   can be defined as   and  . Using the function of the unit circle,  , another equation for the unit circle is found,  . When working with trigonometric functions, it is mainly useful to use angles with measures between 0 and   radians, or 0 through 90 degrees. It is possible to have higher angles than that, however. Using the unit circle, two identities can be found:   and   for any integer  .

The unit circle can substitute variables for trigonometric functions.