Question

X=t cost, y= t+ saint then d^2x/dy^2 at t= pi/2 is equals to

Answer 1

dx/dy = (dx/dt)/(dy/dt)

(cost - t sint)/(1+cost)

d^x/dy^2 = d/dy (dx/dy) = d/dt (dx/dy) dt/dy
= (d/dt (dx/dy))/(dy/dt)
= -(sint(t sint+2) + t cos^2(t) + cost(t+sint))/(1+cost)
at t = pi/2 that is
-(pi/2 + 2)