Trevor Pythagoras

Radians and degrees are both ways of measuring angles. Degrees is the most commonly used and is based on older imperial values, giving it 360 degrees in a circle. Radians are a more mathematical measurement with 2pi radians

A radian is the angle of a sector of a circle where the arc is equal to the radius.
So if the circumference is 2 x pi x r there are 2pi radians in a circle

Also
360^o=2∏ rad
1^o=2∏/360 rad
1^o=∏/180 rad

and
1 rad = 180/∏ ^o

Radians can also be useful to find the length of arcs and the area of sectors.
The length of an arc is the fraction of the circle it is times the circumference so in radians

=(Ø/2pi) x 2pi x r
but the 2pi’s cancel
so
=Ør

The area of a sector is similar but for the area of the circle so
=(Ø/2pi) x pi x r²
=Ør²/2