Polar coordinates are actually an alternative system to the Cartesian coordinates. In two dimensions, they mark a point on a plane by its radial distance (r) from an “origin” and a polar angle (θ). This method also uses trigonometric functions such as sin and cos (sine and cosine; for more about such functions, see trigonometry in this chapter).

Polar coordinates in three-dimensional space—also called spherical coordinates—use r and two polar angles (θ, φ) to give the direction from the origin to the point. To compare, a three-dimensional polar coordinate system overlaps the Cartesian system in several ways: For example, θ is the angle between the line to the origin and the z-axis of the Cartesian (x, y, z) system; φ is the angle (counterclockwise when viewed from positive z) between the projection of that line onto the (x, y) plane and the x-axis.