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: 40

Answer

$\cos$ 100$^{\circ}$$\cos$ 80$^{\circ}$ - $\sin$ 100$^{\circ}$$\sin$ 80$^{\circ}$ $\approx$ 0.99999999 or $\cos$ 100$^{\circ}$$\cos$ 80$^{\circ}$ - $\sin$ 100$^{\circ}$$\sin$ 80$^{\circ}$ $\approx$ 1

Work Step by Step

$\cos$ 100$^{\circ}$$\cos$ 80$^{\circ}$ - $\sin$ 100$^{\circ}$$\sin$ 80$^{\circ}$ Evaluate each piece: $\cos$ 100$^{\circ}$ $\approx$ -0.17364818 $\cos$ 80$^{\circ}$ $\approx$ 0.17364818 $\sin$ 100$^{\circ}$ $\approx$ 0.98480775 $\sin$ 80$^{\circ}$ $\approx$ 0.98480775 Combine: $\cos$ 100$^{\circ}$$\cos$ 80$^{\circ}$ $\approx$ -0.03015369 $\sin$ 100$^{\circ}$$\sin$ 80$^{\circ}$ $\approx$ 0.96984630 -0.03015369 - 0.96984630 $\approx$ 0.99999999 Therefore: $\cos$ 100$^{\circ}$$\cos$ 80$^{\circ}$ - $\sin$ 100$^{\circ}$$\sin$ 80$^{\circ}$ $\approx$ 0.99999999 or $\cos$ 100$^{\circ}$$\cos$ 80$^{\circ}$ - $\sin$ 100$^{\circ}$$\sin$ 80$^{\circ}$ $\approx$ 1
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