Question

What possible advantage might using radians have over using degrees?

Answer 1

The big advantage of using radians is that they're the natural measure for dividing up circles. If you took the radius of a circle and bent it into an arc that lies along the circumference of the circle, you would need a little more than six of them to go all the way around the circle.

Answer 2

for more details check this site http://www.dummies.com/how-to/content/defining-the-radian-in-trigonometry.html

Answer 3

another huge advantage is that if you try to use degrees in calculus you constantly have to do conversions. This is because calculus basically works on pure numbers, and radians actually have no units.