The half angle cosine is given by:
[tex]\begin{gathered} \cos (\frac{\theta}{2})=\sqrt[]{\frac{1+\cos (\theta)}{2}} \\ \end{gathered}[/tex]
The cofunction cosecant is given by:
[tex]\begin{gathered} \csc (\theta)=\frac{1}{\sin (\theta)} \\ \end{gathered}[/tex]
Therefore:
[tex]\begin{gathered} \cos (\frac{\theta}{2})=\sqrt[]{\frac{1+\cos (\theta)}{2}} \\ \frac{1}{\sin (\theta)}=-\frac{6}{5} \\ \sin (\theta)=-\frac{5}{6} \\ \cos (\theta)=\frac{\sqrt[]{6^2-5^2}}{6} \\ \cos (\theta)=\frac{\sqrt[]{11}}{6} \\ \cos (\frac{\theta}{2})=\sqrt[]{\frac{1+\frac{\sqrt[]{11}}{6}}{2}} \\ \cos (\frac{\theta}{2})=\sqrt[]{\frac{\frac{6+\sqrt[]{11}}{6}}{2}} \\ \cos (\frac{\theta}{2})=\sqrt[]{\frac{6+\sqrt[]{11}}{12}} \end{gathered}[/tex]
