Question

Use the given información to find the exact value of the trigonometric function.

Answer 1

The half angle cosine is given by:

`\begin{gathered} \cos ((\theta)/(2))=\sqrt[]{(1+\cos (\theta))/(2)} \\ \end{gathered}`

The cofunction cosecant is given by:

`\begin{gathered} \csc (\theta)=(1)/(\sin (\theta)) \\ \end{gathered}`

Therefore:

`\begin{gathered} \cos ((\theta)/(2))=\sqrt[]{(1+\cos (\theta))/(2)} \\ (1)/(\sin (\theta))=-(6)/(5) \\ \sin (\theta)=-(5)/(6) \\ \cos (\theta)=\frac{\sqrt[]{6^2-5^2}}{6} \\ \cos (\theta)=\frac{\sqrt[]{11}}{6} \\ \cos ((\theta)/(2))=\sqrt[]{\frac{1+\frac{\sqrt[]{11}}{6}}{2}} \\ \cos ((\theta)/(2))=\sqrt[]{\frac{\frac{6+\sqrt[]{11}}{6}}{2}} \\ \cos ((\theta)/(2))=\sqrt[]{\frac{6+\sqrt[]{11}}{12}} \end{gathered}`