Given:
[tex]\sin \theta=\frac{12}{13}[/tex]
For given interval:
[tex]\begin{gathered} 90^{\circ}<\theta>180^{\circ} \\ \sin \theta=\frac{12}{13} \\ \theta=\sin ^{-1}(\frac{12}{13}) \\ \text{for interval} \\ \theta=180-\sin ^{-1}(\frac{12}{13}) \\ \theta=180-67.3801 \\ \theta=112.619 \end{gathered}[/tex]
so
[tex]\begin{gathered} =\cos \theta \\ =\cos (112.619) \\ =-0.3846 \end{gathered}[/tex]
