# Measuring Rotation

## Key Questions

• Negative angles has to do with the direction of rotation that you consider in order to measure angles.

Normally you start counting your angles from the positive side of the x axis in an anti-clockwise direction of rotation:

You can also go clockwise and so to avoid confusion you use a negative sign to indicate this kind of rotation.

• You can draw an angle in standard position by positioning its vertex at the origin and one "ray" on the positive x-axis. The ray on the x-axis is called the initial side and the other ray is called the terminal side.

An angle is then measured POSITIVE for a counterclockwise rotation and NEGATIVE for a clockwise rotation:

When two angles have the same initial and terminal sides, they are said to be coterminal angles.
Angles of −315° and 45° are coterminal angles.

As discussed below.

#### Explanation:

Coterminal Angles are angles who share the same initial side and terminal sides. Finding coterminal angles is as simple as adding or subtracting 360° or 2π to each angle, depending on whether the given angle is in degrees or radians.

For example, the angles 30°, –330° and 390° are all coterminal.

What is the terminal side?
Standard Position of an Angle - Initial Side - Terminal Side. An angle is in standard position in the coordinate plane if its vertex is located at the origin and one ray is on the positive x-axis. The ray on the x-axis is called the initial side and the other ray is called the terminal side.