## Trigonometry 7th Edition

$107^{\circ}$
Given- $\sec\theta$ = - $3.4159$ , $\theta$ belongs to Q II We will find reference angle of $\theta$ first, using calculator in degree mode by the$\frac{1}{x}$ and $\cos^{-1}$ key with the positive value $3.4159$ as $\cos\theta$ = $\frac{1}{\sec\theta}$- $3.4159$ → $\frac{1}{x}$ → $\cos^{-1}$→→ 72.977416435 i.e. reference angle of $\theta$ = $72.977416435^{\circ}$ The desired angle $\theta$ is in Q II, whose reference angle is $73^{\circ}$. Also $0^{\circ}\leq \theta\lt 360^{\circ}$ Therefore- $\theta$ = $180^{\circ} - 72.977416435^{\circ}$ = $107.02258357^{\circ}$ = $107^{\circ}$ (to the nearest tenth of a degree)