What is radian?

Answer 1

"Radian" is an angle, of a very specific size. If you draw a 1-radian angle from the

middle of a circle, then the length of the piece of the circle that it cuts out is exactly

equal to the length of the circle's radius.

Since the length of the circle's full circumferece has 2pi times the radius in it, the full

360 degrees of angle in the circle has 2pi radians in it.

That makes the size of each radian 360/2pi = about 57.3 degrees (an irrational number).

Just reading about it now, you don't see any reason to use an angle with such

a complicated definition, especially if you can never exactly write the number of

degrees in it. But when you get into Physics, Calculus, Electricity, Engineering,

and Trig, this angle starts to pop up everywhere.