detailed description of how to convert an angle from degrees to radians and explain the reasoning for each step of the procedure

Question

 detailed description of how to convert an angle from degrees to radians and explain the reasoning for each step of the procedure

Answer 1

There are 360 degrees in a circle. The reason for this has been lost in history

There are 2pi radians in a circle. The same angle can be measured in either degrees or radians. If the angle measure in degrees in D and the same angle measured in radians is R. Then the fraction of a circle represented by the angle is the same in either case. so

 

D/360 = R/(2pi)

 

or 

 

D = 360(R/(2pi)) or R = (D*(2pi))/360.