A curve is given by $x = 3 \cos t$, $y = 2 \sin t$. What is its slope $\frac{dy}{dx}$ at $t = \frac{\pi}{3}$?

Explanation

1. 01

   $\frac{dx}{dt} = - 3 \sin t$ and $\frac{dy}{dt} = 2 \cos t$.

2. 02

   $\frac{dy}{dx} = \frac{dy/dt}{dx/dt} = - \frac{2}{3 \tan t}$.

3. 03

   At $t = \frac{\pi}{3}$ the slope is $- \frac{2 \sqrt{3}}{9}$.