Find the equation of tangent to the curve x = sin 3t, y = cos 2t at t = π/4.

Question

Find the equation of tangent to the curve x = sin 3t, y = cos 2t at t =\(\frac{\pi}{4}.\)

Answer 1

Here,

y = cos 2t

∴ \(\frac{dy}{dt}\) = - 2sin 2t

Also,

x = sin 3t

∴ \(\frac{dx}{dt}\) = 3 cos 3t

Therefore, equation of tangent at t = \(\frac{\pi}{4}\) i.e., at \((\frac{1}{\sqrt2},0)\) is given by,