## The Lesson

A point can be drawn on a graph. The polar coordinates of the point tell us where to draw the point on the graph. Imagine you wanted to draw a point with polar coordinates**(5, 45°)**.

## How to Draw a Point from Polar Coordinates

Drawing a point from polar coordinates is easy. Polar coordinates have 2 numbers.-
The number on the left (5) is called the radial coordinate. It tells you how far the point is from a reference point (called the
**pole**). -
The number on the right (45°) is called the angular coordinate. It tells you what the angle (in the counter-clockwise direction) the point is from a reference direction (called the
**polar axis**).

## Question

Draw the point with polar coordinates**(5, 45°)**on a graph.

## Step-by-Step:

# 1

Start with a graph.

**Don't forget:**In polar coordinates, there is a reference point (called the**pole**) and a reference direction shown by the horizontal**polar axis**.# 2

Find the first number in the polar coordinates (called the radial coordinate). In our example, the radial coordinate is

**5**.
(

**5**, 45°)# 3

Starting from the pole, count along the polar axis until you find the number found in

**Step 2**(5).# 4

Using a compass, with the compass needle on the pole, draw an arc with a radius given in

**Step 2**(5).# 5

Find the second number in the polar coordinates (called the angular coordinate). In our example, the angular coordinate is

**45°**.
(5,

**45°**)# 6

Using a protractor, measure the angle found in

**Step 5**(45°) in the counter-clockwise direction.# 7

Draw the point where the line from

**Step 6**meets the arc drawn in**Step 4**.## Answer:

## Drawing a Point from Polar Coordinates Using the Polar Grid

A polar grid helps us draw a point from 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 points with the same angular coordinate (because all points on the line are the same angle from the polar axis).

**(5, 45°)**on the polar grid, find the circle with a radius of

**5**and the line at an angle of

**45°**.

We can draw the point straight off, without the use of a compass and protractor:

## What's in a Name?

Polar coordinates are named because Jacob Bernoulli called the point from which other points are measured the**pole**and the horizontal line which passes through it the

**polar axis**. The radial coordinate is sometimes called the

**radius**. The angular coordinate is sometimes called the

**polar angle**or the

**azimuth**.