Study guides › Level 9 · Trigonometry

Quadrants and reference angles

Level 9 · Trigonometry · for questions like “What is the reference angle of 210°?”

💡 The idea

The reference angle is the sharp angle back to the nearest part of the x-axis:

• Quadrant II (90° to 180°): 180° − angle
• Quadrant III (180° to 270°): angle − 180°
• Quadrant IV (270° to 360°): 360° − angle

✏️ Worked examples

1. 210°: quadrant III, so 210 − 180 = 30°.

2. Where is sin positive and cos negative? Quadrant II.

🎯 Try these

1. Reference angle of 135°
2. Reference angle of 300°
3. Where is tan positive and sin negative?

Answers: 1) 45° 2) 60° 3) Quadrant III

This guide is also in the 10MathQ app: tap “📖 Study guide” after a question.