Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 7 - 7.4 - Sum and Difference Formulas - 7.4 Exercises - Page 540: 88


$(-1)^n \sin \theta $

Work Step by Step

By using the Sum and Difference formulas: $\cos (a+b)=\cos a \cos b -\sin a \sin b$ and $\cos (a-b)=\cos a \cos b +\sin a \sin b$ Recall that the sine of a multiple of $\pi$ is always $0$, and the cosine of a multiple of $\pi$ is always $1$ when $n$ is even and $-1$ when $n$ is odd. Therefore, $\sin n \pi \cos \theta +\cos n \pi \sin \theta$ or, $ =(0) \cos \theta +\cos n \pi \sin \theta$ or, $ =\cos n \pi \sin \theta$ or, $=(-1)^n \sin \theta $
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