Radians to Degrees

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 2π.

∴ There are 2π 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°