AHL 3.7 (HL)—Radian measure

One radian is the angle subtended by an arc whose length equals the radius. A full turn is 2π radians, so radians connect angle directly to circle geometry.

Convert degrees using θ(rad)=θ°π/180. In radian measure, arc length is s=rθ and sector area is ½r²θ, with θ in radians.

For r=5 and θ=1.2, the arc length is 6 units and the sector area is 15 square units. Using 1.2° instead would give a completely different scale.

Do not substitute degrees into s=rθ or ½r²θ. Check the angle unit before using a formula.