Geometry and Trigonometry

Analytic Geometry

What are polar coordinates?

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.


This is a web preview of the "The Handy Math Answer Book" app. Many features only work on your mobile device. If you like what you see, we hope you will consider buying. Get the App