# Find the exact value of the trigonometric function cos (9pi)/4.

Find the exact value of the trigonometric function $\frac{\mathrm{cos}\left(9\pi \right)}{4}$.
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Derrick
Rewriting the given trigonometric function,
$\frac{\mathrm{cos}\left(9\pi \right)}{4}=\mathrm{cos}\left(\frac{8\pi +\pi }{4}\right)$
$=\mathrm{cos}\left(\frac{8\pi }{4}+\frac{\pi }{4}\right)$
$=\mathrm{cos}\left(2\pi +\frac{\pi }{4}\right)$
We know that $\left(2\pi +\theta \right)$ always lies in first quadrant and in first quadrant all trigonometric functions are positive.
So applying above rule for the given trigonometric function, we get
$\mathrm{cos}\left(2\pi +\frac{\pi }{4}\right)=\mathrm{cos}\left(\frac{\pi }{4}\right)$
$=\frac{1}{\sqrt{2}}$
Hence, exact value of the given trigonometric function is $\frac{1}{\sqrt{2}}$
Jeffrey Jordon