Coterminal Angles One Positive and One Negative Calculator

What are Coterminal Angles?

Coterminal angles are angles that share the same terminal side when drawn in standard position. They differ by integer multiples of 360° (for degrees) or 2π radians (for radians). For example, 30° and 390° are coterminal because 390° - 360° = 30°.

When working with one positive and one negative angle, you can find coterminal angles by adding or subtracting full rotations until you reach an equivalent angle within the standard range (0° to 360° for degrees, 0 to 2π for radians).

How to Find Coterminal Angles

To find coterminal angles with one positive and one negative angle:

1. Identify the positive and negative angles you want to work with.
2. Add or subtract full rotations (360° or 2π) to find equivalent angles.
3. Repeat the process until you find all desired coterminal angles.

For example, if you have 45° and -315°, you can find coterminal angles by adding 360° to -315° to get 45°, which is coterminal with the original 45°.

Using the Calculator

Our calculator makes it easy to find coterminal angles with one positive and one negative angle. Simply enter your angles in the input fields, select the unit (degrees or radians), and click "Calculate". The calculator will display the coterminal angles and visualize them on a chart.

The calculator shows:

• The original angles you entered
• The calculated coterminal angles
• A visualization of the angles on a unit circle

Examples

Example 1: Degrees

Find coterminal angles for 60° and -300°.

1. Add 360° to -300°: -300° + 360° = 60°
2. 60° is coterminal with the original 60°.

The coterminal angle is 60°.

Example 2: Radians

Find coterminal angles for π/4 and -5π/4.

1. Add 2π to -5π/4: -5π/4 + 2π = 3π/4
2. 3π/4 is coterminal with π/4.

The coterminal angle is 3π/4.