91Ó°ÊÓ

Negative angles are angles measured clockwise from the positive x-axis. Unlike positive angles, which are measured counterclockwise, negative angles go in the opposite direction. In this exercise, we're looking for a negative coterminal angle.

For example, if you start at the positive x-axis and move 50° counterclockwise, you'll land on the angle 50°. However, if you move 50° clockwise instead, you end up with a negative angle, specifically -310°.

Negative angles are a great way to describe direction differently. They are especially useful when dealing with rotations and periodic functions in trigonometry. Remember, a negative angle tells you that your direction is opposite to the usual counterclockwise direction.

Angle subtraction helps us find coterminal angles. Subtracting a full rotation (360°) from an angle lets us explore its coterminal counterpart.

In our exercise, we started with a positive angle of 50°. By subtracting 360° from 50°, we found the coterminal angle: \[50^{\text{°}} - 360^{\text{°}} = -310^{\text{°}}\]

Angle subtraction is essential because it simplifies angle calculations, aiding our understanding of rotational motion and periodic behavior of trigonometric functions.

A full rotation or revolution is an angle of 360°. Adding or subtracting full rotations to a given angle does not change its position in a circular path. It only 'wraps' the angle around a circle.

In cases involving coterminal angles, we often use full rotations to simplify or transform angles without disrupting their terminal side.

For instance, when we subtract 360° from 50° to get -310°, we effectively complete one negative full rotation. The angles 50° and -310° share the same terminal side but are separated by a full rotation.

This concept is crucial because it explains why negative and positive angles can be coterminal and helps visualize angles extending beyond the usual 0° to 360° range.