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: 48

Answer

$\tan19^{\circ}45′$ = 0.3590

Work Step by Step

First we will convert $19^{\circ}45′$ to decimal degrees, let's break it as- $19^{\circ}45′$ = $19^{\circ}$ + $45′$ Now on dividing 45′ by 60, we have the number of "decimal degrees" equivalent to 45′ (as $1^{\circ}$=60′) Therefore $19^{\circ}45′$ = $19^{\circ} + (\frac{45}{60})^{\circ}$ $19^{\circ}45′$ = $19^{\circ} + 0.75^{\circ}$ $19^{\circ}45′$ = $19.75^{\circ}$ Now Using calculator in degree mode- $\tan 19.75^{\circ}$ = 0.3590366866 Rounding it to four places past the decimal point- $\tan 19.75^{\circ}$ = 0.3590 Therefore- $\tan19^{\circ}45′$ = 0.3590
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