Negative angle

Definition

A negative angle is an angle measured clockwise from the positive x-axis. It indicates the direction of rotation in a coordinate plane.

5 Must Know Facts For Your Next Test

1. Negative angles are typically measured in degrees or radians.
2. The sine and cosine functions for negative angles have properties: $\sin(-\theta) = -\sin(\theta)$ and $\cos(-\theta) = \cos(\theta)$.
3. On the unit circle, a negative angle moves in the clockwise direction while a positive angle moves counter-clockwise.
4. A full rotation (360 degrees or $2\pi$ radians) can be split into both positive and negative angles to simplify calculations.
5. Negative angles can often be converted to their positive equivalents by adding or subtracting full rotations ($360^\circ$ or $2\pi$ radians).

Review Questions

• How do you measure a negative angle on the unit circle?
• What is the relationship between $\sin(-\theta)$ and $\sin(\theta)$?
• How can you convert a negative angle to its positive equivalent?

Related terms

Unit Circle: A circle with a radius of one centered at the origin of the coordinate system.

$Radian$: $A measure of an angle where the arc length is equal to the radius of the circle. One full revolution equals $2\pi$ radians.$

$Reference Angle$: $The smallest acute angle formed by the terminal side of an angle and the x-axis.$