[tex]\bf \begin{array}{clclll}
(-2&,&9)\\
\uparrow &&\uparrow \\
x&&y\\
a&&b
\end{array}
\\\\\\
c^2=a^2+b^2\implies c=\sqrt{a^2+b^2}\implies c=\sqrt{(-2)^2+(9)^2}
\\\\\\
c=\sqrt{85}\impliedby
\begin{array}{llll}
\textit{hypotenuse/radius is just a unit}\\
\textit{thus, is never negative}
\end{array}
\\\\\\
cos(\theta)=\cfrac{adjacent}{hypotenuse}\implies cos(\theta)=\cfrac{a}{c}\implies cos(\theta)=\cfrac{-2}{\sqrt{85}}\\\\
-------------------------------\\\\[/tex]
[tex]\bf \textit{now, let's rationalize the denominator}
\\\\\\
\cfrac{-2}{\sqrt{85}}\cdot \cfrac{\sqrt{85}}{\sqrt{85}}\implies \cfrac{-2\sqrt{85}}{85}[/tex]
