Overview
This lecture explains how to convert between degree and radian measures in trigonometry, providing step-by-step examples and key formulas.
Converting Degrees to Radians
- Multiply the degree value by π/180° to convert it to radians.
- The degree unit cancels during multiplication, leaving the answer in radians.
- Example: 325° × π/180° = 65π/36 radians after simplification.
- Example: 60° × π/180° = π/3 radians.
- Example: –315° × π/180° = –7π/4 radians after simplification.
- Example: 570° × π/180° = 19π/6 radians after simplification.
Converting Radians to Degrees
- Multiply the radian value by 180°/π to convert it to degrees.
- The π unit cancels, leaving the answer in degrees.
- Example: (65π/36) × 180°/π = 325°.
- Example: (π/3) × 180°/π = 60°.
- Example: (–4π/3) × 180°/π = –240°.
- Example: (–7π/4) × 180°/π = –315°.
Special Angles and Their Equivalents
- 180° is equal to π radians.
- 30° is equal to π/6 radians (180° ÷ 6).
- 60° is equal to π/3 radians (180° ÷ 3).
Key Terms & Definitions
- Degree (°) — A unit for measuring angles, where a full circle is 360°.
- Radian (rad) — A unit for measuring angles, where a full circle is 2π radians.
- π (pi) — A mathematical constant approximately equal to 3.14159, used in radian measure.
Action Items / Next Steps
- Practice converting between degrees and radians using the formulas discussed.
- Review the equivalence of special angles in both units.
- Prepare questions for clarification if any steps are unclear.