# How do you find the exact value of cos 33pi/4?

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Alan P. Share
Dec 7, 2015

$\cos \left(\frac{33 \pi}{4}\right) = \frac{\sqrt{2}}{2}$

#### Explanation:

$\frac{33 \pi}{4}$ is equivalent to $\frac{32 \pi}{4} + \frac{\pi}{4} = 2 \cdot \left(2 \pi\right) + \frac{\pi}{4} = \frac{\pi}{4} \textcolor{w h i t e}{\text{XX}}$(since $2 \pi = 0$, a complete circle)

$\cos \left(\frac{\pi}{4}\right) = \frac{1}{\sqrt{2}} = \frac{\sqrt{2}}{2} \textcolor{w h i t e}{\text{XXX}}$(this is one of the standard angles)

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