If x=2cos (z) and y= sin (z), then d^2y/dx^2=?

Question

What I got -sin (z) / -8cos (z)*sin (z) simplifies to 1/8cos (z)

I don't think I'm right...

Answer 1

dy/dt = cosz
dx/dt = -2sinz

dy/dx = -1/2 cotz

d^2y/dx^2 = [d/dt(dy/dx)]/(dx/dt)
= -1/2 csc^2(z) / -2sinz
= -1/4 csc^3(z)

too bad you didn't show any of your work...