Reference Angle Calculator
Find the reference angle for any given angle. Enter your angle and select the unit to calculate.
Calculation Steps:
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What is a Reference Angle?
In trigonometry, a reference angle is the acute version of any angle (greater than 90°). It's the size of the smallest acute angle (less than 90°) formed by the terminal side of the angle and the x-axis. Reference angles are always positive and are used to find trigonometric function values of angles in all quadrants.
How to Find a Reference Angle:
- For angles in Quadrant I (0° to 90° or 0 to π/2 radians): The reference angle is the angle itself.
- For angles in Quadrant II (90° to 180° or π/2 to π radians): Reference Angle = 180° - Angle (or π - Angle).
- For angles in Quadrant III (180° to 270° or π to 3π/2 radians): Reference Angle = Angle - 180° (or Angle - π).
- For angles in Quadrant IV (270° to 360° or 3π/2 to 2π radians): Reference Angle = 360° - Angle (or 2π - Angle).
This calculator helps you quickly determine the reference angle for any given angle, making trigonometry problems easier to solve.
Example Formulas:
- Degrees to Radians: $$ Radians = Degrees \times \frac{\pi}{180} $$
- Radians to Degrees: $$ Degrees = Radians \times \frac{180}{\pi} $$
- Reference Angle (Quadrant II): $$ \theta_{ref} = 180° - \theta $$
- Reference Angle (Quadrant III): $$ \theta_{ref} = \theta - 180° $$
- Reference Angle (Quadrant IV): $$ \theta_{ref} = 360° - \theta $$