Question

If x = a sin³t, y = b cos³t then find `dy/dx` at t = `pi/4`

Answer 1

x = a sin³t

`dx/dt=a*3sin^2t*cost`

y = b cos³t

`dy/dt=b*3cos^2t(-sint)`

`dy/dx=(3bcos^2t(-sint))/(3asin^2t*cost)`

= `(–b)/a cos t`

= `(–b)/a cos(pi/4)`

= `(-b)/a(1)`

= `(-b)/a`