Question

For the curve x = a (cosθ + θ sinθ), y = a (sinθ – θcosθ), show that the radius of curvature at ′θ′ varies as θ.

Answer 1

x = a (cosθ + θ sinθ)

⇒ dx/dθ = a (– sinθ + θ cosθ + sinθ) = aθcosθ

= a (sin θ – θ cos θ)

⇒ dy/dθ = a (cosθ + θ sinθ – cosθ) = a θsinθ