Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 2 - Acute Angles and Right Triangles - Section 2.3 Finding Trigonometric Function Values Using a Calculator - 2.3 Exercises: 44

Answer

$\sin$ 28$^{\circ}$ 14' $\cos$ 61$^{\circ}$ 46' + $\cos$ 28$^{\circ}$ 14' sin 61$^{\circ}$ 46' $\approx$ 1

Work Step by Step

$\sin$ 28$^{\circ}$ 14' $\cos$ 61$^{\circ}$ 46' + $\cos$ 28$^{\circ}$ 14' sin 61$^{\circ}$ 46' Convert minutes to decimals: $\frac{14}{60}$ = 0.2333 $\frac{46}{60}$ = 0.7666 Therefore: $\sin$ 28$^{\circ}$ 14' $\cos$ 61$^{\circ}$ 46' + $\cos$ 28$^{\circ}$ 14' sin 61$^{\circ}$ 46' = $\sin$ 28.2333$^{\circ}$ $\cos$ 61.7666$^{\circ}$ + $\cos$ 28.2333$^{\circ}$ sin 61.7666$^{\circ}$ $\sin$ 28.2333$^{\circ}$ $\cos$ 61.7666$^{\circ}$ + $\cos$ 28.2333$^{\circ}$ sin 61.7666$^{\circ}$ $\approx$(0.4731)(0.4731) + (0.8810)(0.8810) $\approx$ 0.2238 + 0.7761 $\approx$ 0.9999 $\approx$ 1 Therefore: $\sin$ 28$^{\circ}$ 14' $\cos$ 61$^{\circ}$ 46' + $\cos$ 28$^{\circ}$ 14' sin 61$^{\circ}$ 46' $\approx$ 1
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