unit circle

A unit circle is a circle of radius 1.

When centered at the origin, the Cartesian coordinates $(x,y)$ satisfy the equation $x^2+y^2=1$.
Visually,

By the definition of the trigonometric functions, the points $(x,y)$ can be equivalently defined by the angle $\theta$ measured counterclockwise from the pole as $(\cos \theta ,\sin \theta )$.

The following figure shows selective angles and their associated points, commonly used in elementary exercises: