​ Find d^2y/dx^2 if. 1. x = a cosθ, y = a sinθ 2. x = a(θ + sinθ), y = a(1 – cosθ) ​

Question

Find \(\frac{d^2y}{dx^2}\) if.

1. x = a cosθ, y = a sinθ 

2. x = a(θ + sinθ), y = a(1 – cosθ) 

3. x = a cos³t, y = -a sin³t

Answer 1

1. Given x = a cos θ, y = a sin θ 

Differentiate both W.r.t. θ

2. Given x = a(θ + sinθ), y = a(1 – cos θ) 

Differentiate both w.r.t θ

3. Given x = a cos³t, y = -a sin³t 

Differentiate both w.r.t t