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: 51

Answer

$\sec 45^{\circ}54′$ = 1.4370

Work Step by Step

First we will convert $45^{\circ}54′$ to decimal degrees, let's break it as- $45^{\circ}54′$ = $45^{\circ}$ + $54′$ Now on dividing 54′ by 60, we have the number of "decimal degrees" equivalent to 54′ (as $1^{\circ}$=60′) Therefore $45^{\circ}54′$ = $45^{\circ} + (\frac{54}{60})^{\circ}$ $45^{\circ}54′$ = $45^{\circ} + 0.9^{\circ}$ $45^{\circ}54′$ = $45.9^{\circ}$ Now Using calculator in degree mode- $\cos 45.9^{\circ}$ = 0.6959127966 $\sec 45.9^{\circ}$ = 1.4369616494 (Using $\frac{1}{x}$ key on calculator) Rounding it to four places past the decimal point- $\sec 45.9^{\circ}$ = 1.4370 Therefore- $\sec 45^{\circ}54′$ = 1.4370
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