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 123: 98


(c). $251^{\circ}$

Work Step by Step

Given- $\cos\theta$ = - $0.3256$ , $\theta$ belongs to Q III and $0^{\circ}\leq \theta\lt 360^{\circ}$ We will find reference angle of $\theta$ first, using calculator in degree mode by the $\cos^{-1}$ key with the positive value $0.3256$- $0.3256$ → $\cos^{-1}$→→ 70.998070238 i.e. reference angle of $\theta$ = $71^{\circ}$ (to the nearest degree) The desired angle $\theta$ is in Q III, whose reference angle is $71^{\circ}$. Also $0^{\circ}\leq \theta\lt 360^{\circ}$ . Therefore- $\theta$ = $ 180^{\circ} + 71^{\circ}$ = $251^{\circ}$
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