Each point in the polar coordinate system can be described with the two polar coordinates, which are usually called r (the radial coordinate) and θ (the angular coordinate, polar angle, or azimuth angle, sometimes represented as φ or t). The r coordinate represents the radial distance from the pole, and the θ coordinate represents the anticlockwise (counterclockwise) angle from the 0°.

For example, the polar coordinates (3, 60°) would be plotted as a point 3 units from the pole on the 60° ray.

Converting between polar and Cartesian coordinates

From polar to cartesian coordinates.

Example 1:

Convert (3, )  into polar coordinates

Solution:

From cartesian to polar coordinates.

Example 2:

Convert (-1,-1) into polar coordinates

Solution:

Circle:

   This is a circle of radius and center (a, b).