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 - Page 71: 72

Answer

$\theta$ = $9^{\circ}9'$

Work Step by Step

Given, $\sec\theta$ = $1.0129$ We will calculate $\cos\theta$ first as calculator does not have $\sec^{-1}$ key. Using reciprocal identity- $\cos\theta$ = $\frac{1}{\sec\theta}$ = $\frac{1}{1.0129}$ Using calculator-(1.0129 → $\frac{1}{x}$) $\cos\theta$ = $0.9872642907$ Therefore- $\theta$ = $\cos^{-1} 0.9872642907$ Given $\theta$ is between $0^{\circ}$ and $90^{\circ}$, i.e. lies in QI Using calculator in degree mode-(0.9872642907 → $\cos^{-1}$) $\theta$ = $(9.1540061634) ^{\circ}$ $\theta$ = $9^{\circ} + (0.1540061634)^{\circ}$ $\theta$ = $9^{\circ} +(0.1540061634\times60)'$ (Recall $1^{\circ}$ = $60'$) $\theta$ = $9^{\circ} +9'$ (Rounding to the nearest minute) $\theta$ = $9^{\circ}9'$
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