Trigonometry (10th Edition)

Published by Pearson

Chapter 2 - Acute Angles and Right Triangles - Section 2.3 Finding Trigonometric Function Values Using a Calculator - 2.3 Exercises: 39

Answer

$\sin$ 35$^{\circ}$$\cos 55^{\circ} + \cos 35^{\circ}$$\sin$ 55$^{\circ}$ $\approx$ 0.99999998 or $\sin$ 35$^{\circ}$$\cos 55^{\circ} + \cos 35^{\circ}$$\sin$ 55$^{\circ}$ $\approx$ 1

Work Step by Step

$\sin$ 35$^{\circ}$$\cos 55^{\circ} + \cos 35^{\circ}$$\sin$ 55$^{\circ}$ Evaluate each piece: $\sin$ 35$^{\circ}$ $\approx$ 0.57357643 $\cos$ 55$^{\circ}$ $\approx$ 0.57357643 $\cos$ 35$^{\circ}$ $\approx$ 0.81915204 $\sin$ 55$^{\circ}$ $\approx$ 0.81915204 Combine: $\sin$ 35$^{\circ}$$\cos 55^{\circ} \approx 0.32898992 \cos 35^{\circ}$$\sin$ 55$^{\circ}$ $\approx$ 0.67101006 0.32898992 + 0.67101006 $\approx$ 0.99999998 Therefore: $\sin$ 35$^{\circ}$$\cos 55^{\circ} + \cos 35^{\circ}$$\sin$ 55$^{\circ}$ $\approx$ 0.99999998 or $\sin$ 35$^{\circ}$$\cos 55^{\circ} + \cos 35^{\circ}$$\sin$ 55$^{\circ}$ $\approx$ 1

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