Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 14 Trigonometric Graphs, Identities, and Equations - 14.6 Apply Sum and Difference Formulas - 14.6 Exercises - Skill Practice - Page 953: 39c


$z^2=r^2 [\cos 2\theta +i \sin 2\theta]$

Work Step by Step

From the previous part (b), we have $z^2=r^2 [\cos \theta \cos \theta - \sin \theta \sin \theta]+i ( \sin \theta \cos \theta+\cos \theta \sin \theta]$ Need to use the formulas such as: $\sin (a+b)= \sin a \cos b+\cos a \sin b$ and $\cos (a+b)= \cos a \cos b- \sin a \sin b$ Thus, we have $z^2=r^2 [\cos (\theta + \theta) +i \sin (\theta + \theta)]$ Hence, $z^2=r^2 [\cos 2\theta +i \sin 2\theta]$
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