Angles

An angle is formed by rotating one ray about a fixed point until it reaches a second ray. If a ray $OA$ is rotated about its endpoint $O$ until it reaches the position $OB$, the angle produced is called $\angle AOB$ (or simply $\theta$).

• $O$, the common point about which the rotation happens, is the vertex of the angle.
• $OA$, the ray in its starting position, is the initial side.
• $OB$, the ray in its final position, is the terminal side.

Sign convention. The direction of rotation matters, not just the amount swept:

• Rotating $OA$ anticlockwise produces a positive angle.
• Rotating $OA$ clockwise produces a negative angle.

This is a real departure from the unsigned "angle between two rays" of elementary geometry — here, the same pair of rays can represent two different angles depending on which way you rotate from one to the other, and, as later sections show, the same terminal position can even be reached by many different amounts of rotation. …