An angle is the union of two rays that share a common endpoint. The
rays are called the sides of the angle, and the common endpoint is the
vertex of the angle. The measure of an angle is the measure of the space
between the rays. It is the direction of the rays relative to one another that
determine the measure of an angle.
In trigonometry, angles are often defined in terms of rotation. Consider one
ray, and then let it rotate a fixed distance about its endpoint. The ray in its
initial position before the rotation, and the ray in its ending, or terminal
position, after the rotation, creates an angle. The endpoint point about which
the ray rotates is the vertex. The amount of rotation determines the measure of
the angle. The ray in the initial position, before the rotation, is called the
initial side of the angle. The ray in the terminal position, after the
rotation, is called the terminal side of the angle. An angle created this
way has a positive measure if the rotation was counterclockwise, and a negative
measure if the rotation was clockwise.
Figure 1.1: An angle defined as the rotation of a single ray
Note that a ray can rotate all the way around to its initial position, and
possibly further, and still result in an angle with an initial and terminal
side. This definition of an angle places no restriction on the magnitude of an
angle (how far it can rotate).
