Trigonometry 7th Edition

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

Chapter 2 - Section 2.2 - Calculators and Trigonometric Functions of an Acute Angle - 2.2 Problem Set: 63

Answer

$\theta$ = $33.3^{\circ}$

Work Step by Step

Given, $\csc\theta$ = $1.8214$ We will calculate $\sin\theta$ first as calculator does not have $\csc^{-1}$ key. Using reciprocal identity- $\sin\theta$ = $\frac{1}{\csc\theta}$ = $\frac{1}{1.8214}$ Using calculator-(1.8214 → $\frac{1}{x}$) $\sin\theta$ = $0.5490282201$ Therefore- $\theta$ = $\sin^{-1} 0.5490282201$ Given $\theta$ is between $0^{\circ}$ and $90^{\circ}$, i.e. lies in QI Using calculator in degree mode-(0.5490282201 → $\sin^{-1}$) $\theta$ = $(33.300370319) ^{\circ}$ On rounding to the nearest tenth of a degree- $\theta$ = $33.3^{\circ}$
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