Study guides › Level 9 · Trigonometry

Degrees and radians

Level 9 · Trigonometry · for questions like “What is 135° in radians?”

💡 The idea

Radians are another way to measure angles. A half turn is 180°, and also π radians. So:

• degrees → radians: × π/180
• radians → degrees: replace π with 180°

✏️ Worked examples

1. 135°: 135/180 = 3/4, so 3π/4.

2. 5π/6: 5 × 180 ÷ 6 = 150°.

⚡ Handy ones

30° = π/6 · 45° = π/4 · 60° = π/3 · 90° = π/2 · 180° = π · 360° = 2π

⚠️ Watch out

• Simplify the fraction: 120/180 = 2/3, so 120° = 2π/3.

🎯 Try these

1. 60° in radians
2. 7π/4 in degrees
3. 210° in radians

Answers: 1) π/3 2) 315° 3) 7π/6

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