Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 7 - Analytic Trigonometry - 7.5 Sum and Difference Formulas - 7.5 Assess Your Understanding - Page 488: 58


Please refer to the step-by-step part below.

Work Step by Step

Recall: (1) $\cos{(\alpha+\beta)}=\cos{(\alpha)}\cos{(\beta)}-\sin{(\alpha)}\sin{(\beta)}$ (2) $\cos{\frac{3\pi}{2}}=0$ and $\sin{\frac{3\pi}{2}}=-1$ Hence, $\cos{(\frac{3\pi}{2}+\theta)}\\=\cos{(\frac{3\pi}{2})}\cos{(\theta)}-\sin{(\frac{3\pi}{2})}\sin{(\theta)}\\=0\cos{(\theta)}-(-1)\cdot \sin{(\theta)}\\ =\sin{(\theta)}$
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