Answer
$314.3^{\circ}$
Work Step by Step
Given-
$\sec\theta$ = $1.4325$ , $\theta$ belongs to Q IV and $0^{\circ}\leq \theta\lt 360^{\circ}$
We will find reference angle of $\theta$ first, using calculator in degree mode by the$\frac{1}{x}$ and $\cos^{-1}$ key with the value $1.4325$ as $\cos\theta$ = $\frac{1}{\sec\theta}$
$1.4325$ → $\frac{1}{x}$ → $\cos^{-1}$→→ 45.726813267
i.e. reference angle of $\theta$ = $45.7^{\circ}$ (to the nearest tenth of a degree)
The desired angle $\theta$ is in Q IV, whose reference angle is $45.7^{\circ}$.
Also $0^{\circ}\leq \theta\lt 360^{\circ}$
Therefore-
$\theta$ = $360^{\circ} - 45.7^{\circ}$
= $314.3^{\circ}$
