Question

what is 2pi/5 in degrees?

Answer 1

Remember that one rotation in radians is 2pi and one rotation in degrees is 360 degrees. So if you set them equal, you'll get a conversion factor out of it by using a little algebra, here I'll show you: \[2\pi \ rad = 360 \ \deg\]So divide both sides by 2pi radians to see how many degrees you get per radian. \[1=\frac{180 \ \deg}{\pi \ rad}\] The interesting thing about this is that multiplying by 1 doesn't change anything, so you can freely convert while knowing it doesn't actually change the value, just its representation. So for instance if you want to convert say, pi/2 radians into degrees as an example to show how it works:
\[\frac{\pi}{2} \ rad *\frac{180 \ \deg}{\pi \ rad}=90 \ \deg\] See how the radians cancelled out just like a number? That's how you know you're doing your conversion correctly.

This is probably one of the most useful and fundamental things to know for every math, physics, chemistry, or science class in general. If you want to understand this better I can help.