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# Degrees to Radians

### 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*°*

##### Degrees To Radians

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

Note: Special measure you will use regularly include –

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### Practice Question

- Convert 150
*°*into radians.

##### Solution

- To convert degrees into radians:

Therefore:

150°=150 x π/180 radians

=150π/180 radians

=5π/6 radians

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