[tex]\bf \textit{Pythagorean Identities} \\\\ sin^2(\theta)+cos^2(\theta)=1 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \begin{cases} x=6cos(t)\\ \cfrac{x}{6}=cos(t)\\[0.5em] \cline{1-1} y=3sin(t)\\ \cfrac{y}{3}=sin(t) \end{cases}\qquad \implies cos^2(t)+sin^2(t)=1 \\\\\\ \left( \cfrac{x}{6} \right)^2+\left( \cfrac{y}{3} \right)^2=1\implies \cfrac{x^2}{6^2}+\cfrac{y^2}{3^2}=1\implies \cfrac{x^2}{36}+\cfrac{y^2}{9}=1[/tex]
