Circular Measure (Copy)

9 Circular Measure – Cheat Sheet

Radian Measure

• 1 radian = angle subtended at centre by arc length equal to radius.
• Conversion:
  • Degrees → Radians: θ (rad) = θ° × π / 180
  • Radians → Degrees: θ° = θ (rad) × 180 / π
• Full circle: 2π rad (360°)
• Half circle: π rad (180°)

Arc Length

• Formula (radians): l = rθ
  • l = arc length
  • r = radius
  • θ = angle in radians

Sector Area

• Formula (radians): A = ½ r² θ
  • A = area of sector
  • r = radius
  • θ = angle in radians

Common Shapes

• Segment area = sector area – triangle area
  • Triangle area (using chord): ½ r² sin θ
• Compound shapes → split into sectors, triangles, rectangles

Quick Checks

• Always use radians in formulas — convert if given degrees
• If θ in radians > 2π → more than 1 full rotation
• Arc length and area are directly proportional to θ for fixed r