# What Are Polar Coordinates?

## What Are Polar Coordinates?

Polar coordinates are used to describe the position of a point on a graph.

The image below shows a graph. A point is plotted on the graph (a blue cross) with its polar coordinates written beside it: (5, 45°). • The pole is a reference point (like an origin).

• The horizontal axis is called the polar axis.

## How Do Polar Coordinates Work?

Polar coordinates work by measuring how far the point is from a reference point (called the pole) and what angle it is from a reference direction (called the polar axis).

• First you measure how far the point is from the pole. This is called the radial coordinate. The point above is 5 units from the pole so its radial coordinate is 5.

• Then you measure the angle of the point (in the counter-clockwise direction) from the polar axis. This is called the angular coordinate. The point above is 45° from the polar axis so its angular coordinate is 45°.

• The radial coordinate (5) and the angular coordinate (45°) are then written in brackets, separated by a comma. The radial coordinate is on the left, the angular coordinate is on the right. ## Polar Coordinates in General

In general, we write polar coordinates as: r is the radial coordinate.

θ is the angular coordinate.

r can taken any positive number. θ can be measured in degrees or in radians and is often limited to a whole rotation (0 to 360° or 0 to 2π radians).

## The Polar Grid

A polar grid helps us use polar coordinates. • The concentric circles show us points with the same radial coordinate (because the circles have the same radius).

• The straight lines show us point with the same angular coordinate (because all points on the line are the same angle from the polar axis).