Question

Evaluate the following expression. Write the exact answer. Do not round. If the value does not exist, write DNE for your answer.COS

Answer 1

Given

`\cos ((5\pi)/(6))`

To evaluate.

Now,

It is given that,

`\cos ((5\pi)/(6))`

Then,

`\begin{gathered} \cos ((5\pi)/(6))=\cos ((6\pi-\pi)/(6)) \\ =\cos (\pi-(\pi)/(6)) \end{gathered}`

Since

`\cos (\pi-\theta)=-\cos \theta`

Then,

`\begin{gathered} \cos ((5\pi)/(6))=\cos (\pi-(\pi)/(6)) \\ =-\cos (\pi)/(6) \\ =-\frac{\sqrt[]{3}}{2} \\ =-0.866025403 \end{gathered}`

Hence, the value is -0.866025403.