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: 81

Answer

$135^{\circ}$

Work Step by Step

Given- $\csc\theta$ = $\sqrt 2$ , $\theta$ belongs to Q II We will find reference angle of $\theta$ first using value $\sqrt 2$ and reference angle theorem- $\csc\theta$ = $\sqrt 2$ = $\csc 45^{\circ}$ (As $\csc 45^{\circ}$ = $\sqrt 2$) Therefore by reference angle theorem, $45^{\circ}$ is the reference angle for desired angle $\theta$ The desired angle $\theta$ is in Q II, Also $0^{\circ}\leq \theta\lt 360^{\circ}$ Therefore- $\theta$ = $180^{\circ} - 45^{\circ}$ = $135^{\circ}$
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