Converting Between Radians and Degrees

Basics

• Revolution of a Circle:
  • 1 revolution = 2π radians = 360°
• Converting formula:
  • π radians = 180°
  • 1 radian = 180/π degrees
  • 1 degree = π/180 radians

Conversion Methodology

• To Convert Degrees to Radians:

  • Multiply the number of degrees by π/180
  • Example: Convert 30° to radians
    • [30 \times \frac{π}{180} = \frac{π}{6} \text{ radians}]

• To Convert Radians to Degrees:

  • Multiply the number of radians by 180/π
  • Example: Convert π/3 radians to degrees
    • [\frac{π}{3} \times \frac{180}{π} = 60°]

Practical Examples

• Convert 45° to radians:
  • [45 \times \frac{π}{180} = \frac{π}{4} \text{ radians}]
• Convert -π/2 radians to degrees:
  • [-\frac{π}{2} \times \frac{180}{π} = -90°]

Key Insight

• Unit Analysis: Helps in ensuring the conversion between degrees and radians is correct. Cancel units to verify results.
• Intuition: The process becomes intuitive with practice by understanding how units cancel out.

Additional Practice

• More examples help with understanding; practice makes it intuitive.

---

These notes provide a structured method to convert between radians and degrees, emphasizing the use of unit analysis and the importance of understanding the relationship between these two measures of angles. Practice is essential to gain intuition and comfort with these conversions.