Trigonometry 7th Edition

Published by Cengage Learning
ISBN 10: 1111826854
ISBN 13: 978-1-11182-685-7

Chapter 3 - Section 3.1 - Reference Angle - 3.1 Problem Set - Page 122: 69

Answer

$236^{\circ}$

Work Step by Step

Given- $\sec\theta$ = - $1.7876$ , $\theta$ belongs to Q III 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 $1.7876$ as $\cos\theta$ = $\frac{1}{\sec\theta}$ $1.7876$ → $\frac{1}{x}$ → $\cos^{-1}$→→ 55.985045761 i.e. reference angle of $\theta$ = $55.985045761^{\circ}$ The desired angle $\theta$ is in Q III, whose reference angle is $55.985045761^{\circ}$. Also $0^{\circ}\leq \theta\lt 360^{\circ}$ Therefore- $\theta$ = $180^{\circ} + 55.985045761^{\circ}$ = $235.98504576^{\circ}$ = $236^{\circ}$ (to the nearest tenth of a degree)
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