📐 Lesson: Rotating Line OP and Quadrants
When an angle is measured from the positive x-axis, the rotating line OP moves counterclockwise for positive angles and clockwise for negative angles.
- Quadrant I: 0° to 90°
- Quadrant II: 90° to 180°
- Quadrant III: 180° to 270°
- Quadrant IV: 270° to 360°
To find the acute angle between OP and the x-axis, subtract the nearest multiple of 90° from the given angle:
- a. 100° → Quadrant II → Acute angle = 180° − 100° = 80°
- b. −100° → Equivalent to 360° − 100° = 260° → Quadrant III → Acute angle = 260° − 180° = 80°
- c. 310° → Quadrant IV → Acute angle = 360° − 310° = 50°
- d. −150° → Equivalent to 360° − 150° = 210° → Quadrant III → Acute angle = 210° − 180° = 30°
🧠 Tip: Always convert negative angles to their positive equivalents by adding 360°, then determine the quadrant and acute angle.