Overview
Measuring angles in radians and finding arc lengths and sector areas.
Radians
A radian is the angle that gives an arc equal to the radius.
- π radians = 180°
- To convert: degrees → radians, × π/180; radians → degrees, × 180/π.
Key formulae (θ in radians)
- Arc length: s = r θ
- Area of a sector: A = ½ r² θ
Worked example
A sector has radius 6 cm and angle 0.5 rad:
- Arc length = 6 × 0.5 = 3 cm
- Area = ½ × 6² × 0.5 = 9 cm²
Common mistakes
- Using these formulae with the angle in degrees — they only work in radians.
Exam tips
- Learn exact radian values: 30° = π/6, 45° = π/4, 60° = π/3, 90° = π/2.