Study guides › Level 9 · Trigonometry

Turning: wheels and clock hands

Level 9 · Trigonometry · for questions like “A wheel with radius 4 inches turns through 3 radians. How far does a point on its rim travel?”

💡 The idea

• In radians, arc length = radius × angle. That's why radians are handy.
• The minute hand turns 6° a minute (360° in 60 minutes).
• The hour hand turns 30° an hour (360° in 12 hours).

✏️ Worked examples

1. Radius 4, 3 radians: 4 × 3 = 12 inches.

2. The minute hand in 25 minutes: 25 × 6 = 150°.

3. The hour hand in 4 hours: 4 × 30 = 120°.

🎯 Try these

1. Radius 7, 5 radians: distance?
2. The minute hand in 40 minutes?
3. The hour hand in 9 hours?

Answers: 1) 35 2) 240° 3) 270°

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