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: 51

Answer

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

Work Step by Step

Use the identity $\sin{(\alpha-\beta)}=\sin{(\alpha)}\cos{(\beta)}-\cos{(\alpha)}\sin{(\beta)}$ to obtain: $\sin{(\pi-\theta)}\\=\sin{(\pi)}\cos{(\theta)}-\sin{(\theta)}\cos{(\pi)}\\=0\cos{(\theta)}-(-1)\cdot \sin{(\theta)}\\=\sin{(\theta)}$
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