parametric equations

Question

Evaluate d^2y/dx^2 of the parametric equation x=cos^2t, y=sin^2t, 0<=t<=180

Answer 1

x=cos²(t), y=sin²(t),

dx/dt=-2sin(t)cos(t), dy/dt=2sin(t)cos(t).

dy/dx=(dy/dt)/(dx/dt)=-1, d²y/dx²=0.

Another way is to rewrite x=½(1+cos(2t)), y=½(1-cos(2t)),

dx/dt=-sin(2t), dy/dt=sin(2t), dy/dx=(dy/dt)/(dx/dt)=-1, d²y/dx²=0.