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,

`(\mathrm dy)/(\mathrm dx)=((\mathrm dy)/(\mathrm dt))/((\mathrm dx)/(\mathrm dt))=(4\sec t\tan t)/(3\sec^2t)=\frac43\sin t`

When
`t=\pi`, we have

`(\mathrm dy)/(\mathrm dx)\bigg|_(t=\pi)=\frac43\sin\pi=0`