# Where exactly do radians come from? [duplicate]

I'm aware that the angle in radians is 1 when the arc length is equal to the radius. However, I wonder if this is exactly where radians come from. Have we set radians like this (like we set $$i^2$$ to $$-1$$) or is there something more to it?

• Amongst other things, the derivatives of the $\sin$ and $\cos$ functions become much easier when the arguments are radians rather than degrees or other unit. May 4 at 22:26