[tex]\bf sin(\theta )=\cfrac{\stackrel{opposite}{3}}{\stackrel{hypotenuse}{5}}\impliedby \textit{let's find the \underline{adjacent side}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2-b^2}=a \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \sqrt{5^2-3^2}=a\implies \pm\sqrt{25-9}=a\implies \pm 4=a \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill cos(\theta )=\cfrac{\stackrel{adjacent}{\pm 4}}{\stackrel{hypotenuse}{5}}~\hfill[/tex]
