1. What is a Reference Angle?

A reference angle is the acute angle formed between the terminal side of a given angle and the x-axis. It's always positive and between 0° and 90°, providing a way to relate trigonometric functions of any angle to those of an acute angle.

2. How Does the Calculator Work?

The calculator uses the reference angle formula for angles in the second quadrant:

Where:

• \( \theta \) — The given angle in degrees

Explanation: This formula specifically calculates the reference angle for angles located in the second quadrant (90° < θ < 180°).

3. Importance of Reference Angles

Details: Reference angles are essential in trigonometry for simplifying calculations, solving trigonometric equations, and understanding the periodic nature of trigonometric functions across all quadrants.

4. Using the Calculator

Tips: Enter the angle in degrees. The calculator assumes the angle is in the second quadrant and will compute the corresponding reference angle.

5. Frequently Asked Questions (FAQ)

Q1: What is a reference angle used for?
A: Reference angles help find trigonometric function values for any angle by relating them to equivalent acute angles in the first quadrant.

Q2: How do reference angles work in different quadrants?
A: The calculation differs by quadrant: Q1: θ, Q2: 180°-θ, Q3: θ-180°, Q4: 360°-θ.

Q3: Are reference angles always acute?
A: Yes, reference angles are always between 0° and 90° (acute angles).

Q4: Why is this calculator specific to second quadrant?
A: This calculator uses the formula 180°-θ which specifically applies to angles in the second quadrant.

Q5: Can reference angles be negative?
A: No, reference angles are always positive acute angles measured from the x-axis.