# How do you find the exact value of cos 5pi/4?

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Alan P. Share
Jun 1, 2016

$\cos \left(\frac{5 \pi}{4}\right) = - \frac{1}{\sqrt{2}} \mathmr{and} - \frac{\sqrt{2}}{2}$

#### Explanation:

$\frac{5 \pi}{4}$ is an angle in Quadrant III and as such (based on CAST) its $\cos$ is negative.

$\frac{5 \pi}{4} = \pi + \frac{\pi}{4}$
So its reference angle is $\frac{\pi}{4}$ which is a standard angle with $\cos \left(\frac{\pi}{4}\right) = \frac{1}{\sqrt{2}}$

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