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: 69

Answer

$\theta$ = $10^{\circ}10'$

Work Step by Step

Given, $\cot\theta$ = $5.5764$ We will calculate $\tan\theta$ first as calculator does not have $\cot^{-1}$ key. Using reciprocal identity- $\tan\theta$ = $\frac{1}{\cot\theta}$ = $\frac{1}{5.5764}$ Using calculator-(5.5764→ $\frac{1}{x}$) $\tan\theta$ = $0.1793271645$ Therefore- $\theta$ = $\tan^{-1} 0.1793271645$ Given $\theta$ is between $0^{\circ}$ and $90^{\circ}$, i.e. lies in QI Using calculator in degree mode-(0.1793271645→ $\tan^{-1}$) $\theta$ = $(10.166628552) ^{\circ}$ $\theta$ = $10^{\circ} + (0.166628552)^{\circ}$ $\theta$ = $10^{\circ} +( 0.166628552\times60)'$ (Recall $1^{\circ}$ = $60'$) $\theta$ = $10^{\circ} +10'$ (Rounding to the nearest minute) $\theta$ = $10^{\circ}10'$
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