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A-level Maths
Radians: arcs, sectors, segments & small-angle approximations
Drag point B on the circle (or use the sliders) to change angle θ in radians and degrees. Watch arc length l = rθ, sector area ½r²θ, segment area ½r²(θ − sin θ), and the small-angle approximations update live.
2. Small-angle approximations (as θ → 0 in radians)
Error grows with θWhen θ is small and measured in radians, the arc length θ, vertical height sin θ and tangent height tan θ on the unit circle are almost equal: sin θ ≈ θ, tan θ ≈ θ, and cos θ ≈ 1 − ½θ².