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 an integer multiple of 360° (or 2π radians).

2. How Does the Calculator Work?

The calculator uses the coterminal angle formula:

Where:

• \( \theta_{cot} \) — Coterminal angle (degrees)
• \( \theta \) — Original angle (degrees)
• \( k \) — Any integer

Explanation: Adding or subtracting full rotations (360°) to an angle produces coterminal angles.

3. Importance of Coterminal Angles

Details: Coterminal angles share the same trigonometric function values (sine, cosine, tangent, etc.), making them useful for simplifying angle calculations and solving trigonometric equations.

4. Using the Calculator

Tips: Enter the original angle in degrees, select whether to add or subtract rotations, and specify how many full rotations (k) to apply. The calculator shows both the exact coterminal angle and its normalized version (0-360°).

5. Frequently Asked Questions (FAQ)

Q1: Can coterminal angles be negative?
A: Yes, coterminal angles can be negative when you subtract enough rotations from a positive angle.

Q2: How many coterminal angles does an angle have?
A: An infinite number, since you can add or subtract any integer multiple of 360°.

Q3: What's the difference between reference angles and coterminal angles?
A: Reference angles are always between 0° and 90° and represent the smallest angle to the x-axis, while coterminal angles share the same terminal side.

Q4: Do coterminal angles have the same trigonometric values?
A: Yes, all trigonometric functions (sin, cos, tan, etc.) have identical values for coterminal angles.

Q5: How are coterminal angles used in real-world applications?
A: They're used in navigation, engineering, physics, and anywhere periodic phenomena or rotational systems are involved.