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: 71

Answer

$\theta$ = $8^{\circ}8'$

Work Step by Step

Given, $\csc\theta$ = $7.0683$ We will calculate $\sin\theta$ first as calculator does not have $\csc^{-1}$ key. Using reciprocal identity- $\sin\theta$ = $\frac{1}{\csc\theta}$ = $\frac{1}{7.0683}$ Using calculator-(7.0683 → $\frac{1}{x}$) $\sin\theta$ = $0.1414767342$ Therefore- $\theta$ = $\sin^{-1} 0.1414767342$ Given $\theta$ is between $0^{\circ}$ and $90^{\circ}$, i.e. lies in QI Using calculator in degree mode-(0.1414767342 → $\sin^{-1}$) $\theta$ = $(8.1333075009) ^{\circ}$ $\theta$ = $8^{\circ} + (0.1333075009)^{\circ}$ $\theta$ = $8^{\circ} +(0.1333075009\times60)'$ (Recall $1^{\circ}$ = $60'$) $\theta$ = $8^{\circ} +8'$ (Rounding to the nearest minute) $\theta$ = $8^{\circ}8'$
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