What is the general formula to convert radians to degrees and vice versa?

see explanation

##color(blue)( " to convert radians to degrees")##

( angle in radians) ## xx 180/pi ##

example: convert ## pi/2 color(black)(" radians to degrees ")##

angle in degrees ##= cancel(pi)/2 xx 180/cancel(pi) =180/2 = 90^@##

##color(red)(" to convert degrees to radians") ##

(angle in degrees)## xx pi/180 ##

example : convert 90º to radians

angle in radians = ##cancel (90) xx pi/cancel(180) =pi/2 ##