Coterminal Angles, Reference Angles, Angles of Rotation

Front

What are coterminal angles?

Back

Coterminal angles are angles that share the same terminal side when drawn in standard position. They can be found by adding or subtracting multiples of 360° (or 2π radians) to/from the angle.

Front

How do you find a positive coterminal angle for a given angle?

Back

To find a positive coterminal angle, add 360° (or 2π radians) to the given angle until the result is positive.

Front

How do you find a negative coterminal angle for a given angle?

Back

To find a negative coterminal angle, subtract 360° (or 2π radians) from the given angle until the result is negative.

Front

What is the reference angle?

Back

The reference angle is the acute angle formed by the terminal side of an angle and the x-axis. It is always positive and less than 90°.

Front

How do you find the reference angle for an angle in standard position?

Back

1. If the angle is in the first quadrant, the reference angle is the angle itself. 2. If in the second quadrant, subtract the angle from 180°. 3. If in the third quadrant, subtract 180° from the angle. 4. If in the fourth quadrant, subtract the angle from 360°.

Front

What is the coterminal angle of 240°?

Back

The positive coterminal angle of 240° is 240° + 360° = 600° and the negative coterminal angle is 240° - 360° = -120°.

Front

What is the coterminal angle of -90°?

Back

The coterminal angle of -90° is -90° + 360° = 270° and -90° - 360° = -450°.

Front

How do you convert a negative angle to a positive angle?

Back

To convert a negative angle to a positive angle, add 360° (or 2π radians) until the angle is positive.

Front

What is the angle of rotation?

Back

The angle of rotation is the measure of the angle through which a point or line has been rotated about a fixed point, usually measured in degrees or radians.

Front

How do you approximate the angle of rotation?

Back

To approximate the angle of rotation, determine the angle's position relative to the x-axis and express it in degrees or radians.