Find dy/dx, when If x = cos t and y = sin t, prove that dy/dx = 1/√3 at 1 = 2π/3.

Question

Find \(\cfrac{dy}{d\mathrm x} \), when

If x = cos t and y  = sin t, prove that \(\cfrac{dy}{d\mathrm x} \) = \(\cfrac{1}{\sqrt3}\) at 1 = \(\cfrac{2\pi}3\).

Answer 1

as x = cost

Differentiating it with respect to t,

And, y = sin t

Differentiating it with respect to t,

Dividing equation (2) by (1),