if the angle is an acute angle, meaning is less than 90°, that simply means that θ is in the I quadrant, therefore, its adjacent side is positive, thus
[tex]\bf sin(\theta )=\cfrac{\stackrel{opposite}{12}}{\stackrel{hypotenuse}{13}}\impliedby \textit{now, let's find the \underline{adjacent side}}
\\\\\\
\textit{using the pythagorean theorem}\\\\
c^2=a^2+b^2\implies \pm\sqrt{c^2-b^2}=a
\qquad
\begin{cases}
c=hypotenuse\\
a=adjacent\\
b=opposite\\
\end{cases}[/tex]
[tex]\bf \pm\sqrt{13^2-12^2}=a\implies \pm\sqrt{169-144}=a\implies \pm\sqrt{25}=a
\\\\\\
\pm 5=a\implies \stackrel{I~quadrant}{+5=a}\qquad therefore\qquad
cot(\theta )=\cfrac{\stackrel{adjacent}{5}}{\stackrel{opposite}{12}}[/tex]
