$\mathrm{x}=3 \cos \mathrm{\theta }, \mathrm{y}=3 \sin \mathrm{\theta }, \mathrm{then} \frac{\mathrm{dy}}{\mathrm{dx}}=$

$\mathrm{x}=3 \cos \mathrm{\theta }$                              $\mathrm{y}=3 \sin \mathrm{\theta }$

     $\frac{\mathrm{dx}}{\mathrm{d\theta }}=-3 \sin \mathrm{\theta }$              $\frac{\mathrm{dy}}{\mathrm{d\theta }}=3 \cos \mathrm{\theta }$

      $\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{\mathrm{dy}}{\mathrm{d\theta }}/\frac{\mathrm{dx}}{\mathrm{d\theta }}$

     $=\frac{3 \cos \mathrm{\theta }}{-3 \sin \mathrm{\theta }}=-\cot \mathrm{\theta }$