THE RADIAN
 

The standard unit of plane angular measure is the radian (rad). It is the angle subtended by an arc on a circle whose length, as measured on the circle, is equal to the radius of the circle as measured on a flat geometric plane containing the circle. Imagine taking a string and running it out from the center of a circle to some point on the edge and then laying that string down around the periphery of the circle. The resulting angle is 1 rad. Another 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 the same length r (Fig.1). It is equal to about 57.2958 angular degrees.

Fig. 1. One radian is the angle at the apex of a slice of pie whose straight and curved edges all have the same length r.