Question

Consider the parametric curve:

x = 3 tant

y = 4 sect

find d y / d x at t = π.

Answer 1

By the chain rule,

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\frac{\mathrm dy}{\mathrm dt}}{\frac{\mathrm dx}{\mathrm dt}}=\dfrac{4\sec t\tan t}{3\sec^2t}=\dfrac43\sin t$

When $t=\pi$, we have

$\dfrac{\mathrm dy}{\mathrm dx}\bigg|_{t=\pi}=\dfrac43\sin\pi=0$