# How do you find the exact value of arctan(cos 0)?

Sep 11, 2015

$\arctan \left(\cos \left(0\right)\right) = \frac{\pi}{4}$

#### Explanation:

$\cos \left(0\right) = 1$

if $\theta = \arctan \left(1\right)$
$\textcolor{w h i t e}{\text{XXXX}} \rightarrow \tan \left(\theta\right) = 1$
and since, by definition, $\arctan \in \left[0 , \pi\right]$
the only value that meets this requirement is
$\textcolor{w h i t e}{\text{XXXX}} \theta = \frac{\pi}{4}$