1. What is a Negative Coterminal Angle?

A negative coterminal angle is an angle that shares the same terminal side as the original angle but is measured in the negative (clockwise) direction. It can be found by subtracting multiples of 360° from the original angle.

2. How Does the Calculator Work?

The calculator uses the negative coterminal angle formula:

Where:

• \( \theta \) — Original angle in degrees
• \( n \) — Number of full rotations (must be positive integer)

Explanation: The formula subtracts complete 360° rotations from the original angle to find equivalent angles measured in the negative direction.

3. Importance of Coterminal Angles

Details: Coterminal angles are important in trigonometry as they share the same trigonometric function values (sine, cosine, etc.). Negative coterminal angles are particularly useful when working with angles in the clockwise direction or when simplifying angle measurements.

4. Using the Calculator

Tips: Enter the original angle in degrees and the number of full rotations you want to subtract. The calculator will show the resulting negative coterminal angle.

5. Frequently Asked Questions (FAQ)

Q1: Can I find multiple negative coterminal angles?
A: Yes, by changing the value of n (number of rotations), you can find infinitely many negative coterminal angles.

Q2: What's the difference between positive and negative coterminal angles?
A: Positive coterminal angles are found by adding multiples of 360°, while negative ones are found by subtracting multiples of 360°.

Q3: Can I use this for radians?
A: This calculator works with degrees. For radians, you would subtract multiples of 2π instead of 360°.

Q4: What's the smallest negative coterminal angle?
A: The smallest (least negative) is found by subtracting just enough 360° rotations to get the angle between -360° and 0°.

Q5: Why are coterminal angles important?
A: They simplify angle calculations in trigonometry by allowing equivalent angle representations, especially useful in periodic functions.