If x = a (θ - sin θ) and y = a (1 - cos θ), find y2 at θ - Maths - Continuity and Differentiability

Question

If x = a (θ - sin θ) and y = a (1 - cos θ),
find y2 at θ =

Varun.Rawat · Accepted Answer

We have,x = aθ - sin θ⇒dxdθ = a1 - cos θy = a1 - cos θ⇒dydθ = a0 + sin θ = a sin θdydx = dydθ×dθdx = a sin θa1 - cos θ = sin θ1 - cos θ⇒dydx = 2 sin θ2 cos θ22 sin2θ2 = cot θ2⇒d2ydx2 = -12 cosec2θ2 dθdx⇒d2ydx2 = -12 cosec2θ2 × 1a1 - cos θ⇒d2ydx2θ=π = -12cosec2π2 × 1a1 - cos π =-12×1×12a = -14a

If x = a (θ - sin θ) and y = a (1 - cos θ), find y2 at θ = .

If x = a (θ - sin θ) and y = a (1 - cos θ), find y₂ at θ = .