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: 47

Answer

$\tan42^{\circ}15′$ = 0.9083

Work Step by Step

First we will convert $42^{\circ}15′$ to decimal degrees, let's break it as- $42^{\circ}15′$ = $42^{\circ}$ + $15′$ Now on dividing 15′ by 60, we have the number of "decimal degrees" equivalent to 15′ (as $1^{\circ}$=60′) Therefore $42^{\circ}15′$ = $42^{\circ} + (\frac{15}{60})^{\circ}$ $42^{\circ}15′$ = $42^{\circ} + 0.25^{\circ}$ $42^{\circ}15′$= $42.25^{\circ}$ Now Using calculator in degree mode- $\tan 42.25^{\circ}$ = 0.9083360465 Rounding it to four places past the decimal point- $\tan 42.25^{\circ}$ = 0.9083 Therefore- $\tan42^{\circ}15′$ = 0.9083
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