An angle in standard position has its vertex at the origin and its initial side along the positive x-axis. The terminal side determines the quadrant.
Quadrant Rules:
• Quadrant I: \(0° < \theta < 90°\) or \(0 < \theta < \frac{\pi}{2}\)
• Quadrant II: \(90° < \theta < 180°\) or \(\frac{\pi}{2} < \theta < \pi\)
• Quadrant III: \(180° < \theta < 270°\) or \(\pi < \theta < \frac{3\pi}{2}\)
• Quadrant IV: \(270° < \theta < 360°\) or \(\frac{3\pi}{2} < \theta < 2\pi\)
• Quadrantal angles: \(0°, 90°, 180°, 270°, 360°\) (or \(0, \frac{\pi}{2}, \pi, \frac{3\pi}{2}, 2\pi\)) lie on the axes.
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)