Answer
$\theta$ = $22.2^{\circ}$
Work Step by Step
Given, $\sec\theta$ = $1.0801$
We will calculate $\cos\theta$ first as calculator does not have $\sec^{-1}$ key.
Using reciprocal identity-
$\cos\theta$ = $\frac{1}{\sec\theta}$ = $\frac{1}{1.0801}$
Using calculator-(1.0801 → $\frac{1}{x}$)
$\cos\theta$ = $0.9258402$
Therefore-
$\theta$ = $\cos^{-1} 0.9258402$
Given $\theta$ is between $0^{\circ}$ and $90^{\circ}$, i.e. lies in QI
Using calculator in degree mode-(0.9258402 → $\cos^{-1}$)
$\theta$ = $(22.204607102) ^{\circ}$
On rounding to the nearest tenth of a degree-
$\theta$ = $22.2^{\circ}$
