Answer
$\theta \approx 58.7^o$
Work Step by Step
RECALL:
$\sec{\theta} = \dfrac{1}{\cos{\theta}}$
A calculator does not have a secant function but has cosine and inverse cosine functions.
Solve for $\cos{\theta}$ to obtain:
$\sec{\theta} = \dfrac{1}{\cos{\theta}}
\\1.923 = \dfrac{1}{\cos{\theta}}$
Cross-multiply to obtain:
$1.923\cos{\theta} = 1$
Divide 1.923 to both sides of the equation to obtain:
$\cos{\theta} = \dfrac{1}{1.923}$
Solve for the value of $\theta$ using the inverse cosine function of the calculator to obtain:
$\theta = \cos^{-1}{\left(\dfrac{1}{1.923}\right)}=58.99935321^0 \approx 58.7^o$
