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: 61

Answer

$\theta$ = $11.1^{\circ}$

Work Step by Step

Given, $\sec\theta$ = $1.0191$ Using reciprocal identity- $\cos\theta$ = $\frac{1}{\sec\theta}$ = $\frac{1}{1.0191}$ Using calculator-(1.0191 → $\frac{1}{x}$) $\cos\theta$ = $0.9812579727$ Therefore- $\theta$ = $\cos^{-1} 0.9812579727$ Given $\theta$ is between $0^{\circ}$ and $90^{\circ}$, i.e. lies in QI Using calculator in degree mode-(0.9812579727 → $\cos^{-1}$) $\theta$ = $(11.110319609) ^{\circ}$ On rounding to the nearest tenth of a degree- $\theta$ = $11.1^{\circ}$
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