Any real number may be interpreted as the radian measure of an
angle as follows: If , think of wrapping a length of string
around the standard unit circle C in the plane, with initial
point P(1,0), and proceeding counterclockwise around the circle;
do the same if , but wrap the string clockwise around the
circle. This process is described in Figure 1 below. If Q(x,y)
is the point on the circle where the string ends, we may think
of as being an angle by associating to it the central angle with
vertex O(0,0) and sides passing through the points P and Q. If
instead of wrapping a length s of string around the unit circle,
we decide to wrap it around a circle of radius R, the angle (in
radians) generated in the process will satisfy the following
relation: Observe that the length s of string gives the measure
of the angle only when R=1. As a matter of common practice and
convenience, it is useful to measure angles in degrees, which
are defined by partitioning one whole revolution into 360 equal
parts, each of which