# How do you find the exact value of cos 5pi/3?

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Jim G. Share
Apr 30, 2016

$\frac{1}{2}$

#### Explanation:

The angle $\frac{5 \pi}{3} \text{ is located in the 4th quadrant }$

where the cos ratio has a positive value.

The 'related' acute angle is $\left(2 \pi - \frac{5 \pi}{3}\right) = \frac{\pi}{3}$

and so $\cos \left(\frac{5 \pi}{3}\right) = \cos \left(\frac{\pi}{3}\right)$

Using the $\textcolor{b l u e}{\text{ Exact value triangle for this angle}}$

$\Rightarrow \cos \left(\frac{5 \pi}{3}\right) = \cos \left(\frac{\pi}{3}\right) = \frac{1}{2}$

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