# What Are Polar Co-ordinates? (Mathematics Lesson)

# 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

Step 2

**radius**.

Step 3

**angle**.

Step 3

**( radius, angle )**

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

Step 2

##### Quick Test

**show**

##### Note

**WHAT'S IN A NAME?**

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

**poles**.

The radius is sometimes called the

**radial co-ordinate**.

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.