Trigonometry (10th Edition)

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

Chapter 2 - Acute Angles and Right Triangles - Section 2.2 Trigonometric Functions of Non-Acute Angles - 2.2 Exercises: 54

Answer

False

Work Step by Step

$\sin$ 30$^{\circ}$ + $\sin$ 60$^{\circ}$ = $\sin$(30$^{\circ}$ + 60$^{\circ}$) $\sin$ 30$^{\circ}$ = $\frac{1}{2}$ $\sin$ 60$^{\circ}$ = $\frac{\sqrt3}{2}$ $\sin$ 30$^{\circ}$ + $\sin$ 60$^{\circ}$ = $\frac{1}{2}$ + $\frac{\sqrt3}{2}$ $\sin$ 30$^{\circ}$ + $\sin$ 60$^{\circ}$ = $\frac{1 + \sqrt3}{2}$ $\sin$(30$^{\circ}$ + 60$^{\circ}$) = $\sin$ 90$^{\circ}$ $\sin$ 90$^{\circ}$ = 1 Thus: $\frac{1 + \sqrt3}{2}$ $\ne$ 1 Therefore, $\sin$ 30$^{\circ}$ + $\sin$ 60$^{\circ}$ = $\sin$(30$^{\circ}$ + 60$^{\circ}$) is a false statement.
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