1) Let's use a trigonometric identity for this question:
[tex]\begin{gathered} \cos (2\theta)=1-2\sin ^2(\theta) \\ \cos (2\theta)=1-2\cdot(\frac{-2\sqrt[]{13}}{13})^2 \end{gathered}[/tex]
Notice that for that double angle identity, we need to pick the one that relates the value of the sin(theta):
[tex]\begin{gathered} \cos (2\theta)=1-2\cdot(\frac{-2\sqrt[]{13}}{13})^2 \\ \cos (2\theta)=1-2(\frac{52}{169}) \\ \cos (2\theta)=1-2(\frac{4}{13}) \\ \cos (2\theta)=1-\frac{8}{13}=\frac{5}{13} \end{gathered}[/tex]
2) In Quadrant IV the sign of the cosine function is :
