# 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 ${\displaystyle x^{2}+y^{2}=1}$. The unit circle is centered at the Origin, or coordinates (0,0). It is often used in Trigonometry.

## Trigonometric functions in the unit circle

In a unit circle, where ${\displaystyle t}$  is the angle desired, ${\displaystyle x}$  and ${\displaystyle y}$  can be defined as ${\displaystyle \cos(t)=x}$  and ${\displaystyle \sin(t)=y}$ . Using the function of the unit circle, ${\displaystyle x^{2}+y^{2}=1}$ , another equation for the unit circle is found, ${\displaystyle \cos ^{2}(t)+\sin ^{2}(t)=1}$ . When working with trigonometric functions, it is mainly useful to use angles with measures between 0 and ${\displaystyle \pi \over 2}$  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: ${\displaystyle \cos(t)=\cos(2\cdot \pi k+t)}$  and ${\displaystyle sin(t)=\sin(2\cdot \pi k+t)}$  for any integer ${\displaystyle k}$ .