The Polar Coordinate System describes points in space using a radius and angle relative to the origin. Angles are measured using radians, where a full rotation around the circle is equal to the circle constant τ (tau) or approximately 6.283 radians. By convention angles are measured from what is considered the positive direction in the cartesian-coordinate-system with the positive angle direction as counter-clockwise.

A point is denoted with two variables: which represents the radius corresponding to the point and which represents the angle corresponding to the point.

The point as shown in figure below is an example of how a point is defined in the polar coordinate system. The radius defines the distance form the origin and the angle represents the measured angle. In this case the angle is of a full rotation around the circle.

Note In math there are two systems for measuring angles: degrees and radians.

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.

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 circle constant τ (tau) is a geometric constant approximately equal to 6.283. The numeric value is defined as the length of any circle's circumference divided by the length of its radius.

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.

Degrees are a unit of measure for angles. A full rotation is equal to 360 degrees. In the XY Cartesian Coordinate System, degrees are measured starting from the rightmost edge of the circle.