Unit Circle Physics

This figure illustrates the shape of a vector in the cartesian coordinate plane.
Figure 1: Vector

The properties of the unit circle are used in physics for decomposing vectors into their components. For example, say we want to calculate the components of a velocity vector given its speed and direction. The trigonometry of the unit circle allows us to decompose the vector into its horizontal velocity using its speed (magnitude) denoted and direction (angle) . This is shown below.