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: 65

Answer

$\theta$ = $55.5^{\circ}$

Work Step by Step

Given, $\cot\theta$ = $0.6873$ We will calculate $\tan\theta$ first as calculator does not have $\cot^{-1}$ key. Using reciprocal identity- $\tan\theta$ = $\frac{1}{\cot\theta}$ = $\frac{1}{0.6873}$ Using calculator-(0.6873 → $\frac{1}{x}$) $\tan\theta$ = $1.4549687182$ Therefore- $\theta$ = $\tan^{-1} 1.4549687182$ Given $\theta$ is between $0^{\circ}$ and $90^{\circ}$, i.e. lies in QI Using calculator in degree mode-(1.4549687182→ $\tan^{-1}$) $\theta$ = $(55.499259022) ^{\circ}$ On rounding to the nearest tenth of a degree- $\theta$ = $55.5^{\circ}$
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