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# Radians to Degrees

Theory & Practice Questions.

## Theory

##### Radian, a circle measure

One radian is the angle that an arc of 1 unit subtends at the centre of a circle of radius 1 unit.

Degrees to radians conversion:  1 degrees = π/180 radians

## Radians and Degrees

π^c = 180°

where π^c  = π  radians

## Relationship between radian measure and degrees

Circumference of the circle with radius 1 unit is given by:

C = 2πr

= 2π(1)

= 2π

T

The arc length of the whole circle is .

There are radians in a whole circle.

But there are 360° in a whole circle (angle of revolution).

So 2π^c = 360°

π^c = 180°

## Radians to Degrees

To change from radians to degrees: multiply by 180/π

Note: Special measure you will use regularly include -

## Practice Question

1. Convert 5π/6 radians into degrees.
##### Solution
1. To convert radians into degrees:

Therefore:

5π/6 radians = 180/π° x 5π/6

Simplyfying:

=900π/6π°

=150°

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