Here is what we know:
360° = 2π Radians
Divide both sides by 360:
1° = π/180 Radians
Or, if we had divided both sides by 2π we get:
1 Radian = 180°/π
These equations give us our conversion factors…
To convert from degrees to radians:
degrees * (π/180) = radians
Example: Covert 120 degrees to radians:
120 * π/180 = 120π/180 = 2π/3
So, 120 degrees = 2π/3 radians.
To convert from radians to degrees:
radians * (180/π) = degrees
Example: Covert 5π/6 radians to degrees:
5π/6 * (180/π) = 900π/(6π) = 150
So, 5π/6 radians = 150 degrees.