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: 43

Answer

$\cos$ 75$^{\circ}$ 29' $\cos$ 14$^{\circ}$ 31' - $\sin$ 75$^{\circ}$ 29' $\sin$ 14$^{\circ}$ 31' $\approx$ 0

Work Step by Step

$\cos$ 75$^{\circ}$ 29' $\cos$ 14$^{\circ}$ 31' - $\sin$ 75$^{\circ}$ 29' $\sin$ 14$^{\circ}$ 31' Convert minutes to decimals: $\frac{29}{60}$ = 0.4833 $\frac{31}{60}$ = 0.5166 Therefore: $\cos$ 75.4833$^{\circ}$ $\cos$ 14.5166$^{\circ}$ - $\sin$ 75.4833$^{\circ}$ $\sin$ 14.5166$^{\circ}$ Utilizing a calculator: $\cos$ 75.4833$^{\circ}$ $\cos$ 14.5166$^{\circ}$ - $\sin$ 75.4833$^{\circ}$ $\sin$ 14.5166$^{\circ}$ $\approx$ (0.2506)(0.96800) - (0.9680)(0.2506) $\approx$ 0.2426 - 0.2426 $\approx$ 0 Therefore: $\cos$ 75$^{\circ}$ 29' $\cos$ 14$^{\circ}$ 31' - $\sin$ 75$^{\circ}$ 29' $\sin$ 14$^{\circ}$ 31' $\approx$ 0
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