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: 78



Work Step by Step

Given- $\tan\theta$ = $\frac{\sqrt 3}{3}$ , $\theta$ belongs to Q III We will find reference angle of $\theta$ first using value $\frac{\sqrt 3}{3}$ and reference angle theorem- $\tan \theta$ = $\frac{\sqrt 3}{3}$ = $\tan 30^{\circ}$ (As $\tan 30^{\circ}$ = $\frac{\sqrt 3}{3}$ ) Therefore by reference angle theorem, $30^{\circ}$ is the reference angle for desired angle $\theta$ The desired angle $\theta$ is in Q III, Also $0^{\circ}\leq \theta\lt 360^{\circ}$ Therefore- $\theta$ = $180^{\circ} + 30^{\circ}$ = $210^{\circ}$
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