# How do you find the exact value of cos(arctan (5/2))?

$\cos \left(\arctan \left(\frac{5}{2}\right)\right) = \frac{2 \sqrt{29}}{29}$

#### Explanation:

Let $A$ be an angle whose tangent$= \frac{5}{2}$

Let $A = \arctan \left(\frac{5}{2}\right)$

Then $\tan A = \frac{5}{2}$

Imagine a right triangle with opposite side $a = 5$ and adjacent side $b = 2$. Compute hypotenuse $c$

$c = \sqrt{{a}^{2} + {b}^{2}}$

$c = \sqrt{{5}^{2} + {2}^{2}}$

$c = \sqrt{29}$

Then, the cosine function of $A$

$\cos A = \frac{b}{c} = \frac{2}{\sqrt{29}} = \frac{2 \sqrt{29}}{29}$

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