Coterminal Angle Between 0 and 360 Calculator

What Are Coterminal Angles?

Coterminal angles are angles that have the same terminal side when drawn in standard position. In other words, they are angles that differ by a full rotation (360°) or an integer multiple of 360°. For example, 45° and 405° are coterminal because 405° - 360° = 45°.

Coterminal angles are useful in trigonometry because they allow us to simplify angle measurements. Any angle can be expressed as a coterminal angle between 0° and 360° by adding or subtracting multiples of 360°.

How to Find Coterminal Angles

To find coterminal angles between 0° and 360° for a given angle θ, follow these steps:

1. If θ is positive, subtract 360° until the result is between 0° and 360°.
2. If θ is negative, add 360° until the result is between 0° and 360°.
3. If the result is already between 0° and 360°, it is the coterminal angle.

This process ensures that you find the equivalent angle within one full rotation (0° to 360°).

Using the Calculator

Our coterminal angle calculator makes it easy to find all coterminal angles between 0° and 360° for any given angle. Simply enter the angle in the input field and click "Calculate". The calculator will display the coterminal angle and provide a visual representation of the angle on a unit circle.

The calculator also shows the formula used and explains the result in plain English. This makes it easy to understand how the calculation is performed and what the result means.

Example Calculations

Let's look at a few examples to see how the calculator works.

Example 1: Positive Angle

If you enter 405° in the calculator, it will find the coterminal angle between 0° and 360° by subtracting 360°:

405° - 360° = 45°

So, 45° is the coterminal angle between 0° and 360° for 405°.

Example 2: Negative Angle

If you enter -90° in the calculator, it will find the coterminal angle between 0° and 360° by adding 360°:

-90° + 360° = 270°

So, 270° is the coterminal angle between 0° and 360° for -90°.