The

**unit circle**is a concept of mathematics (used in several contexts, especially in trigonometry). In essence, this is a circle constituted by all points that have Euclidean distance 1 from the origin (0,0) in a two-dimensional coordinate system. It is denoted by

*S*

^{1}.

Image:UnitCircle.png

The equation defining the points (*x*, *y*) of the unit circle is

## Trigonometric functions in the unit circle

In a unit circle, several interesting things relating to trigonometric functions may be defined, with the given notation:

A point on the unit circle, pointed to by a certain vector from the origin with the angle from the -axis has the coordinates:

- and for any integer
*n*.

*x*,

*y*) coordinates remain the same after the angle

*t*is increased or decreased by one revolution in the circle (2π). The notion of sine, cosine, and other trigonometric functions only makes sense with angles more than zero or less than π/2 when working with right triangles, but in the unit circle, angles outside this range have sensible, intuitive meanings.