# Polar Coordinate System

The Polar Coordinate System describes points in space using an angle and radius relative to the origin. Angles are measured using radians, where a full rotation around the circle is equal to approximately 6.283 radians or τ (tau) radians. A point is denoted in the same fashion as the cartesian coordinate system. The first component represents the radius of the point, and the second component represents the angle of the point.

The interactive graphic below demonstrates a point in the polar coordinate system. Click and drag the blue control point to see how its position is represented.

Radians are a unit that measure angle using the radius of a circle. One radian is equal to the amount of rotation required to travel the length of one radius along the circumference of the circle.

The Cartesian Coordinate System describes space of one, two, and three dimensions. Each point in space is represented by its distance relative to the origin of the system.

To convert a point from the Polar Coordinate System to the Cartesian Coordinate System the functions sine and cosine are used to calculate the x and y component of the corresponding point.

To convert a point from polar coordinates to cartesian coordinates, the trigonometric functions cosine and sine can be used.