The reference angle is the acute angle between the terminal side of the given angle and the x-axis. It is always between 0° and 90° (or 0 and \( \frac{\pi}{2} \) radians).
Rules for finding the reference angle:
• Quadrant I: reference angle = angle
• Quadrant II: reference angle = 180° - angle (π - angle)
• Quadrant III: reference angle = angle - 180° (angle - π)
• Quadrant IV: reference angle = 360° - angle (2π - angle)
For quadrantal angles (0°, 90°, 180°, 270°, 360°), the reference angle is 0° or 90°.
Quadrant I: 0° to 90° (0 to π/2) | Quadrant II: 90° to 180° (π/2 to π)
Quadrant III: 180° to 270° (π to 3π/2) | Quadrant IV: 270° to 360° (3π/2 to 2π)
Axes: 0°, 90°, 180°, 270°, 360° (0, π/2, π, 3π/2, 2π) are quadrantal angles.