Radians to degrees

Question

I am having a bit of a blank moment, when converting radians to degrees you know that, 2 x pi x radians = 360 degrees.

so that pi x radians  = 180 degrees. Which should mean that radians on its own is equal to 180/pi x degrees . However when you do the calculation and make the angle as 57.3 degrees which should be 1 radian you actually get 3283. So the correct equation should be radians = pi/180 x degrees. But I don't understand how you would get to that equation thank you using formulas. 

Answer 1

 

 pi = 180 

2*pi = 360

 

1 radian = 180/pi which is APPROXIMATELY (not EXACTLY) 57.3 degrees

 

and pi/180 = 1 degree

 

So 57.3 degrees is APPROXIMATELY (not EXACTLY) pi*57.3/180 = 1 degree with some roundoff digits

 

 

 

 

 

Answer 2

360 degrees = 2π radians

 

Therefore if you have an angle in radians and want it in degrees, multiply the angle you have by 360/2π.

 

If you want to go the other way, i.e. degrees to radians, multiply the angle in degrees by 2π/360.

 

I hope that helps.  Just a general helpful note: when doing unit conversions, what will almost always help get the right answer is to make the units work...e.g. degrees/radians * radians = degrees.