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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 = 2*πr*

= 2*π*(1)

= 2*π*

T

The arc length of the whole circle is *2π*.

*∴* There are *2π* radians in a whole circle.

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

So 2*π**^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 –

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### Practice Question

- Convert 5
*π*/6 radians into degrees.

##### Solution

- To convert radians into degrees:

Therefore:

5*π*/6 radians = 180/π*°* x 5π/6

Simplyfying:

=900π/6π*°*

=150*°*

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