Answer
$\theta$ = $11.1^{\circ}$
Work Step by Step
Given, $\sec\theta$ = $1.0191$
Using reciprocal identity-
$\cos\theta$ = $\frac{1}{\sec\theta}$ = $\frac{1}{1.0191}$
Using calculator-(1.0191 → $\frac{1}{x}$)
$\cos\theta$ = $0.9812579727$
Therefore-
$\theta$ = $\cos^{-1} 0.9812579727$
Given $\theta$ is between $0^{\circ}$ and $90^{\circ}$, i.e. lies in QI
Using calculator in degree mode-(0.9812579727 → $\cos^{-1}$)
$\theta$ = $(11.110319609) ^{\circ}$
On rounding to the nearest tenth of a degree-
$\theta$ = $11.1^{\circ}$
