# How do you find the value for cos (cos^-1 (3/4))?

${\cos}^{- 1} \left(x\right)$ or $\arccos \left(x\right)$ (to avoid confusion as to an interpretation as a possible negative exponent)
$\textcolor{w h i t e}{\text{XXXX}}$$=$the angle $\theta$ for which $\cos \left(\theta\right) = x$ (basic definition)
Therefore $\cos \left(\arccos \left(\frac{3}{4}\right)\right)$
$\textcolor{w h i t e}{\text{XXXX}}$= cos(the angle $\theta$ for which cos(theta) = 3/4 )
$\textcolor{w h i t e}{\text{XXXX}}$$= \frac{3}{4}$