The Radian:

The standard unit of plane angular measure is the radian (i.e., rad). It is the angle subtended by an arc on a circle whose length, as measured on the circle, is equivalent to the radius of the circle as measured on a flat geometric plane having the circle. Visualize taking a string and running it out from the center of a circle to a few points on the edge and then laying that string down about the periphery of the circle. The resultant angle is 1 rad. The other definition goes like this: One radian is the angle between the two straight edges of a slice of pie whose straight and curved edges all have similar length r which is as shown in figure below. It is equivalent to around 57.2958 angular degrees.

Figure: One radian is the angle at the apex of a slice of pie whose straight and curved edges all have similar length r.