Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 5 - Section 5.2 - Sum and Difference Formulas - Exercise Set - Page 672: 111

Answer

a) No. b) Yes.

Work Step by Step

a)$$\sin 60^{\circ } = \sin ( 2 \cdot 30^{\circ })=\frac{\sqrt{3}}{2}, \quad \sin 30^{\circ }= \frac{1}{2} \\ \Rightarrow \quad \sin ( 2 \cdot 30^{\circ })= \frac{\sqrt{3}}{2} \neq 1=2(\frac{1}{2})= 2 \sin 30^{\circ }$$ b)$$\sin 60^{\circ } = \sin ( 2 \cdot 30^{\circ })=\frac{\sqrt{3}}{2}, \quad \sin 30^{\circ }= \frac{1}{2}, \quad \cos 30^{\circ }=\frac{\sqrt{3}}{2} \\ \Rightarrow \quad \sin ( 2 \cdot 30^{\circ })= \frac{\sqrt{3}}{2} =2(\frac{1}{2})(\frac{\sqrt{3}}{2})= 2 \sin 30^{\circ } \cos 30^{\circ }$$
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