In order to convert from radians to degrees, you multiply the radians by 180 degrees / pi radians?

Question

Ok, so I just had a very confusing lecture.

Is it true that to convert from radians to degrees you multiply the radians by 180 degrees over pi radians?

Answer 1

That is correct. I'm not clear on what you find confusing. The basic fact is that 180 degrees is the same as 3.14159263... radians. That's just like the fact that 10 miles is the same as 16.09 km. You could also say that 360 degrees = 2π radians. It works out the same.



Here are two ways to think about the conversion:



1. Units. If you have a value in radians, and you multiply it by degrees / radians, the radians cancel out and you are left with degrees.



2. Ratios. 180 degrees is the same as π radians. That means that each radian is 180/pi or 57.30 degrees. You multiply the number of radians by this to get the number of degrees.



Radians are strange units. It seems like it would be more convenient to have a full circle be 1 unit instead of 2π units, but radians turn out to be extremely convenient units.

Answer 2

True, because 180 degrees = pi radians

Answer 3

no, to go from degrres to radians you just multiply by pi ONLY

Answer 4

180/π; yes.



e.g.

π/3

=>180π/3π=60