1. What is a Coterminal Angle?

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:

• \( \theta \) — Original angle (degrees or radians)
• \( k \) — Any integer (positive, negative, or zero)
• 360° — Full rotation in degrees
• \( 2\pi \) — Full rotation in radians

Explanation: Adding or subtracting full rotations (360° or 2π) to any angle results in an angle that shares the same terminal side.

3. Importance of Coterminal Angles

Details: Coterminal angles are essential in trigonometry as they share the same trigonometric function values (sine, cosine, tangent, etc.). They're used to simplify angle measurements and find equivalent angles within a specific range.

4. Using the Calculator

Tips: Enter the original angle, select the unit (degrees or radians), and specify the integer multiplier (k). Positive k gives counterclockwise rotations, negative k gives clockwise rotations.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between reference and coterminal angles?
A: Reference angles are always between 0-90° and measure the smallest angle to the x-axis. Coterminal angles share the same terminal side but can be any size.

Q2: How many coterminal angles does an angle have?
A: Infinite! You can add or subtract any number of full rotations (360° or 2π).

Q3: What's the principle coterminal angle?
A: The angle between 0-360° (or 0-2π) that's coterminal with the original angle.

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

Q5: How are coterminal angles used in real life?
A: They're used in navigation, engineering, physics, and anywhere periodic phenomena are analyzed.