## Trigonometry 7th Edition

$314.3^{\circ}$
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- $\theta$ = $360^{\circ} - 45.7^{\circ}$ = $314.3^{\circ}$