# What does cos(arctan((-3pi)/4))  equal?

$\cos \left(\arctan \left(\frac{- 3 \pi}{4}\right)\right) = \frac{4}{\sqrt{16 + 9 {\pi}^{2}}}$

#### Explanation:

We are looking for the cosine function of an angle A. The angle A whose tangent =$\frac{- 3 \pi}{4}$

$A = \arctan \left(\frac{- 3 \pi}{4}\right)$ it is an angle

Just imagine a right triangle with angle A with opposite side $= - 3 \pi$
and with adjacent side $= 4$. Then we have a hypotenuse $= \sqrt{{4}^{2} + {\left(- 3 \pi\right)}^{2}} = \sqrt{16 + 9 {\pi}^{2}}$

$\cos A = \frac{4}{\sqrt{16 + 9 {\pi}^{2}}}$