Given:
[tex]\cos \theta\text{ =- }\frac{1}{8}[/tex]
Solving for the angle measure:
[tex]\begin{gathered} \theta\text{ = }\cos ^{-1}(-\frac{1}{8}) \\ =\text{ }97.181 \end{gathered}[/tex]
Hence, we can find the exact value of sin theta:
[tex]\begin{gathered} But\text{ }\theta\text{ is in the third quadrant.} \\ \sin (97.181\text{ -180) = sin(-82.8190}) \\ =\text{ -0.992} \end{gathered}[/tex]
Hence, the exact value of sin theta is -0.992
