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: 60

Answer

True

Work Step by Step

$\sin$(2 * 30$^{\circ}$) = 2 $\sin$ 30$^{\circ}$ * $\cos$ 30$^{\circ}$ First evaluate the value of each trigonometric statement: $\sin$ (2 * 30$^{\circ}$) = $\sin$ 60$^{\circ}$ = $\frac{\sqrt3}{2}$ $\sin$ 30$^{\circ}$ = $\frac{1}{2}$ $\cos$ 30$^{\circ}$ = $\frac{\sqrt3}{2}$ Next evaluate each side of the equation: $\sin$( 2 * 30$^{\circ}$) = $\frac{\sqrt3}{2}$ 2 $\sin$ 30$^{\circ}$ * $\cos$ 30$^{\circ}$ = 2($\frac{1}{2}$)($\frac{\sqrt3}{2}$) = $\frac{\sqrt3}{2}$ Therefore: $\sin$(2 * 30$^{\circ}$) = 2 $\sin$ 30$^{\circ}$ * $\cos$ 30$^{\circ}$ is a true statement.
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