[tex]\bf \begin{array}{clclll}
(-5&,&-6)\\
x&&y\\
a&&b
\end{array}\qquad c^2=a^2+b^2\implies c=\sqrt{a^2+b^2}
\\\\\\
c=\sqrt{(-5)^2+(-6)^2}\implies c=\sqrt{61}\impliedby
\begin{array}{llll}
c\ is\ never\\
negative
\end{array}
\\\\\\
cos(\theta)=\cfrac{adjacent}{hypotenuse}\implies sin(\theta)=\cfrac{-5}{\sqrt{61}}
\\\\
-------------------------------\\\\
\textit{now, rationalized}
\\\\\\
\cfrac{-5}{\sqrt{61}}\cdot \cfrac{\sqrt{61}}{\sqrt{61}}\implies \cfrac{-5\sqrt{61}}{61}[/tex]
