# Introduction

In this activity you will:

- learn about a new unit to measure angles called
**radians**; - find out how to convert angles given in degrees to radians and vice versa.

# One radian

You need to move the green point until the length of the dark blue line is $$1$$.

The angle you can see is $$1$$ radian.

It's important to be able to measure angles in radians.

Some things are easier working in radians.

Other things, such as differentiation, will only work if using radians!

On the right, the dark blue line is part of circle with radius $$1$$.

The two light blue lines are radii of the circle.

The length of the dark blue line is given.

You can move the green point.

Move it until the dark blue line has length $$1$$.

Then **Submit**.

Created with GeoGebra

# Full circle

You need to increase the angle to a 'full turn'.

Because the circle has radius $$1$$, the circumference of the circle is $$2 \pi$$.

This means that a full turn, $$360^{\circ}$$, is the same as $$2 \pi$$ radians, and $$\pi$$ radians is a half turn or $$180^{\circ}$$.

Here you will look at angles up to a 'full turn' as measured in radians.

On the right, you see part of a circle with radius $$1$$.

Use the 'increase angle' button to enlarge the angle to a 'full turn'.

As you pass through certain angles their size will be displayed in radians.

Notice that the size of the angle is the length of the arc.

Leave the angle so that it is a 'full turn' and then **Finish**.

Created with GeoGebra

# Degrees and radians

You need to increase the angle to a 'half turn'.

Next you'll think about a general rule for converting between degrees and radians.

Here you will look at angles up to a 'half turn' in both degrees and radian.

Remember that a 'half turn' is $$\pi$$ radians.

Therefore a right angle is $$\Large\frac{\pi}{2}$$ radians.

The 'increase' button makes the angle shown larger by $$22.5^{\circ}$$.

Use it to increase the angle to a 'half turn'.

Some key angles will be shown in both degrees and radians as you do this.

Then **Finish**.

Created with GeoGebra

# Converting

Test your answer on the angles shown.

It's important to be familiar with how to convert between radians and degrees.

Here you will think about how to convert an angle given in radians to degrees and vice versa.

The examples you saw on the last page are given on the top at the right.

Answer both of the questions on the right by ticking the boxes then **Submit**.

Created with GeoGebra

# Trig graphs in both units

It's worth trying to be as familiar as you can be with degrees and radians and converting between them, particularly for some of the standard angles.

Everything you know about trigonometric functions, such as solving equations, will work the same in radians.

Familiarity with the graphs in both radians and degrees will help you to feel confident about this.

Here you can compare the graphs of trig functions in degrees and in radians.

Tick whichever trigonometric functions you would like to see and choose units of either degrees or radians.

**Finish** when you are ready to move on.

Created with GeoGebra

# Finally...

Youâ€™ve now completed this activity. Go and explore the other resources!

In this walkthrough you have learned:

- about a new unit to measure angles called
**radians**; - to convert an angle in degrees to an angle in radians divide it by $$180$$ and then multiply by $$\pi$$;
- to convert an angle in degrees to an angle in radians divide it by $$\pi$$ and then multiply by $$180$$.