Polar coordinates

Like any other coordinate, a polar coordinate describes a position on a 2D plane.

A polar coordinate is described by:

• the distance from the origin
• the bearing of the point from the origin

Describing the bearing

We usually use radians to describe the bearing of a polar point from the origin, but technically we could also use degrees.

The bearing starts from the line which extends from the origin to the right: called the initial line On a cartesian system, this would be the ‘positive X’ line.

Common bearings

Knowing that the bearing starts from the line extending to the right, we can say that:

• The line going to the right from the origin is at a bearing of 0\pi radians
• The line going upwards from the origin is at a bearing of \frac12\pi radians
• The line going to the left from the origin is at a bearing of \pi radians
• The line going downwards from the origin is at a bearing of \frac32\pi radians

More simply in a table:

Format of a polar coordinate

We write the polar coordinate in the form (r,\theta), where:

• r is the distance from the origin
• \theta is the bearing of the point from the origin, measured in radians
  • It’s usually between 0 and 2\pi