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: 49

Answer

$\sin 56^{\circ}40′$ = 0.8355

Work Step by Step

First we will convert $56^{\circ}40′$ to decimal degrees, let's break it as- $56^{\circ}40′$ = $56^{\circ}$ + $40′$ Now on dividing 40′ by 60, we have the number of "decimal degrees" equivalent to 40′ (as $1^{\circ}$=60′) Therefore $56^{\circ}40′$ = $56^{\circ} + (\frac{40}{60})^{\circ}$ $56^{\circ}40′$ = $56^{\circ} + 0.6667^{\circ}$ $56^{\circ}40′$ = $56.6667^{\circ}$ Now Using calculator in degree mode- $\sin 56.6667^{\circ}$ = 0.8354881311 Rounding it to four places past the decimal point- $\sin 56.6667^{\circ}$ = 0.8355 Therefore- $\sin 56^{\circ}40′$ = 0.8355
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