Radians · Year 13
In Year 13 you learn: arc length and sector area in radians.
Radians are another way of measuring angles, based on the radius: one radian is the angle that cuts off an arc equal in length to the radius. A full turn is 2π radians, and in radians the arc and sector formulas become much simpler.
Key facts
- π radians = 180°, so 2π = 360°.
- Degrees → radians: × (π)/180. Radians → degrees: × 180/π.
- Arc length s = rθ (θ in radians).
- Sector area A = ½r²θ (θ in radians).
- Segment area = ½r²(θ − sin θ).
Worked examples
Example 1
A sector has radius 8 cm and an angle of 1.2 radians. Find its arc length and its area.
Answer: Arc 9.6 cm, area 38.4 cm²
Example 2
A chord makes an angle of 2 radians at the centre of a circle of radius 5 cm. Find the area of the minor segment, to 1 d.p.
Answer: 13.6 cm²