# What Are Polar Co-ordinates?

Polar co-ordinates can be used to describe a point, called a pole, on a graph.

Polar co-ordinates are described by a pair of numbers in a bracket, separated by a comma.

• The number on the left gives the radius: how far the pole from the origin.

• The number on the right gives the angle: the angle of the pole from the horizontal axis.

# How to Describe a Point in Cartesian Co-ordinates

Question: What are the polar co-ordinates of the point shown on the graph below?

Step 1
Draw a line from the origin to the pole.

Step 2
Find the length of the line. This is the radius.

Step 3
Find the angle of the line from the horizontal axis. This is the angle.

Step 3
Write the polar co-ordinates as

The co-ordinate is (5,45°).

# How to Draw a Pole in Polar Co-ordinates

Question: Draw the pole described by the polar co-ordinates (3,30°) on a graph.

Step 1
Draw a line at the angle from the horizontal axis.

Step 2
Along this line, measure a length 3 from the origin. The pole described by the polar co-ordinates is found at the end of this line.

show

##### Note
WHAT'S IN A NAME?

Polar co-ordinates are so named because the points are called poles.

The angle is sometimes called the angular co-ordinate, the polar angle or the azimuth.

WHY USE POLAR CO-ORDINATES?

Polar co-ordinates are useful when dealing with circular geometry.

For instance, all the poles that can be drawn on a circumference of a circle have the same radius, but lie at difference angles.

For example, a circle of radius 2:

DON'T MIX UP THE CO-ORDINATES

An easy mistake to make is to mix up the radius and the angle.

• The co-ordinate on the left is the radius.

It describes how far from the origin the pole is.

• The co-ordinate on the right is the angle.

It describes the angle of the pole from the horizontal axis.