Learn it
A radian is the angle that cuts off an arc equal in length to the radius. A full circle is 2π radians = 360°, so π radians = 180°.
- Degrees → radians: multiply by π/180.
- Radians → degrees: multiply by 180/π.
In radians, arc length s = rθ and sector area = ½r²θ.
Worked examples
Example 1
Convert 150° to radians.
- 150 × π/180
- = 15π/18 = 5π/6
Answer: 5π/6
Example 2
Find the arc length when r = 10 cm and θ = π/4.
- s = rθ
- 10 × π/4
Answer: 5π/2 ≈ 7.85 cm
Practice
Try these on paper first, then check your work.
- 90° in radians
- 2π/3 in degrees
- 1 radian in degrees (approx.)
- Arc length: r = 6, θ = 2
Show the answer key
- π/2
- 120°
- ≈ 57.3°
- 12