Answer
$\theta\approx 73.26^o$
Work Step by Step
RECALL:
(1) $\theta = \text{arcsec}{(x)}\longrightarrow \sec{\theta}=x$
(2) $\sec{x} =\frac{1}{\cos{x}}$
This means that
$\theta=\text{arcsec}(x)
\\\longrightarrow \sec{\theta}=x
\\\longrightarrow \cos{\theta}=\frac{1}{x}$
Thus,
$\theta =\text{arcsec}(3.4723155)
\\\longrightarrow\sec{\theta}=3.4723155
\\\longrightarrow \cos{\theta} = \frac{1}{3.4723155}$
Use the inverse cosine function of a scientific calculator in degree mode to obtain:
$\theta = \arccos{\left(\frac{1}{3.4723155}\right)}
\\\theta=73.26220613^o
\\\theta\approx 73.26^o$
