Understanding Radians

Introduction

• Radians can be understood by thinking of slicing a pizza.
• Presenter: Tammy - Math enthusiast.

Circumference of the Circle

• Formula: 2πr
• Unit Circle:
  • Radius = 1
  • Circumference = 2π
  • A full circle in radians = 2π

Comparing Radians and Degrees

• Full circle in degrees = 360°
• Full circle in radians = 2π
• Half circle = π

Dividing the Circle

• Unit Circle: Has 16 key points.
• Start at 0 (also 2π after one full rotation).

Halving the Circle

• Divide the circle in half:
  • Half = π
• Divide π in half:
  • π/2, 1/2 π
  • Count: π/2, 2π/2, 3π/2 (fourth point)

Points Based on 30° Angles

• 180° = π radians
• Top half of the circle:
  • Contains six 30° angles
  • Each sector = π/6
• Angles:
  1. 1π/6
  2. 2π/6 → Simplified to π/3
  3. 3π/6 → Simplified to π/2
  4. 4π/6 → Simplified to 2π/3
  5. 5π/6
  6. 6π/6 → Simplified to π
  7. 7π/6
  8. 8π/6 → Simplified to 4π/3
  9. 9π/6 → Simplified to 3π/2
  10. 10π/6 → Simplified to 5π/3
  11. 11π/6
  12. 12π/6 → Simplified to 2π

Points Based on 45° Angles

• 180° = π radians
• Each sector = π/4
• Angles:
  1. π/4
  2. 2π/4 → Simplified to π/2
  3. 3π/4
  4. 4π/4 → Simplified to π
  5. 5π/4
  6. 6π/4 → Simplified to 3π/2
  7. 7π/4
  8. 8π/4 → Simplified to 2π

Conclusion

• This method helps easily determine radian measures on the unit circle.
• Next step involves finding coordinates for each point on the circle.