We have the following:
[tex]\begin{gathered} \sin \theta=-\frac{8}{17} \\ \theta=\sin ^{-1}(-\frac{8}{17}) \\ \theta=-28.07 \end{gathered}[/tex]
now, in Quadrant III (180° to 270°):
[tex]\theta=180+28.07=208.7[/tex]
now, for cosine:
[tex]\cos 2\theta=\cos (2\cdot208.7)=0.538=\frac{539}{1000}[/tex]
The answer is 539/1000
