1. What Are Coterminal Angles?

Coterminal angles are angles in standard position (angles with the initial side on the positive x-axis) that have a common terminal side. They differ by a full rotation of 360° or any integer multiple of 360°.

2. How Does the Calculator Work?

The calculator uses these simple formulas:

Where:

• \( \theta \) — The original angle in degrees
• 360° — One full rotation

Explanation: Adding or subtracting 360° gives you angles that share the same terminal side as the original angle.

3. Importance of Coterminal Angles

Details: Coterminal angles are important in trigonometry because they have identical trigonometric function values (same sine, cosine, tangent, etc.). This property is useful for simplifying angle measurements and solving trigonometric equations.

4. Using the Calculator

Tips: Enter any angle in degrees (positive or negative, whole number or decimal). The calculator will show you one positive and one negative coterminal angle by adding and subtracting 360° respectively.

5. Frequently Asked Questions (FAQ)

Q1: Are there multiple coterminal angles for a given angle?
A: Yes, there are infinitely many coterminal angles. You can add or subtract any multiple of 360° to find more coterminal angles.

Q2: What's the difference between reference angles and coterminal angles?
A: Reference angles are always between 0° and 90° and represent the smallest angle between the terminal side and the x-axis. Coterminal angles share the same terminal side but can be any size.

Q3: Do coterminal angles work in radians?
A: Yes, the concept is the same but you use 2π radians (equivalent to 360°) instead.

Q4: How are coterminal angles used in real life?
A: They're used in navigation, engineering, and physics where angle measurements might need to be simplified or normalized.

Q5: Can an angle be coterminal with itself?
A: Yes, every angle is coterminal with itself (when you add 0 × 360°).