A radian is the angle made when the arc length equals the radius. A full turn is 2π radians, so π radians = 180°. To convert degrees to radians, multiply by π/180.
In radians the formulas are simpler: arc length = rθ and sector area = ½r²θ. A sector of radius 14 cm and angle 1.4 radians has area ½ × 196 × 1.4 = 137.2 cm². Make sure your calculator is in radian mode when using sin, cos and tan with radians.
Worked example
A sector has radius 3 cm and arc length 5π/2 cm. Find its angle.
- Arc length = rθ, so 5π/2 = 3θ.
- θ = 5π/6.
Answer:5π/6 radians
Key words
- radian
- the angle where arc length equals radius
- arc length
- rθ
- sector area
- ½r²θ
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Common Core-referenced: HSF-TF.A.1, HSG-C.B.5