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

$\cos (\frac{5\pi}{6})$

To evaluate.

Now,

It is given that,

$\cos (\frac{5\pi}{6})$

Then,

$\begin{gathered} \cos (\frac{5\pi}{6})=\cos (\frac{6\pi-\pi}{6}) \\ =\cos (\pi-\frac{\pi}{6}) \end{gathered}$

Since

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

Then,

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

Hence, the value is -0.866025403.