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: 70

Answer

$\theta$ = $12^{\circ}12'$

Work Step by Step

Given, $\cot\theta$ = $4.6252$ We will calculate $\tan\theta$ first as calculator does not have $\cot^{-1}$ key. Using reciprocal identity- $\tan\theta$ = $\frac{1}{\cot\theta}$ = $\frac{1}{4.6252}$ Using calculator-(4.6252→ $\frac{1}{x}$) $\tan\theta$ = $0.2162068667$ Therefore- $\theta$ = $\tan^{-1} 0.2162068667$ Given $\theta$ is between $0^{\circ}$ and $90^{\circ}$, i.e. lies in QI Using calculator in degree mode-(0.2162068667→ $\tan^{-1}$) $\theta$ = $(12.199956965) ^{\circ}$ $\theta$ = $12^{\circ} + (0.199956965)^{\circ}$ $\theta$ = $12^{\circ} +(0.199956965\times60)'$ (Recall $1^{\circ}$ = $60'$) $\theta$ = $12^{\circ} +12'$ (Rounding to the nearest minute) $\theta$ = $12^{\circ}12'$
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