General Angle

Initial Ray and Terminal Ray

When two rays and in a plane form an angle , the magnitude of is determined by the amount of rotation of ray from the fixed position of ray around point . In this context, ray is called the initial ray, and ray is called the terminal ray.

When ray rotates around point , counterclockwise rotation is defined as the positive direction, and clockwise rotation is defined as the negative direction. The magnitude of the angle is expressed with a positive sign for counterclockwise rotation and a negative sign for clockwise rotation.

• The initial ray is the ray from which the angle starts, and the terminal ray is the one that moves.
• When representing the magnitude of an angle, the positive sign is often omitted.
  
  

General Angle

If the magnitude of the angle formed by the initial ray and the terminal ray is , then the magnitude of can be expressed as:

This is called the general angle represented by terminal ray .

Since the initial ray is fixed, once the angle’s magnitude is given, the position of the terminal ray is uniquely determined. However, even if the position of the terminal ray is fixed, the magnitude of the angle can vary depending on the number of rotations and the direction. For example, when the terminal ray is at a position from the initial ray , the magnitude of the angle can be expressed in several ways, as shown in the following diagram.

Thus, , , and can all be expressed in the form of the general angle , where is an integer.