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 487: 26



Work Step by Step

Recall that $\sin(\alpha-\beta)=\sin(\alpha)\cos(\beta)-\cos(\alpha)\sin(\beta)$. Hence, $\sin(20^\circ)\cos(80^\circ)+\cos(80^\circ)\sin(20^\circ)=\sin(20^\circ-80^\circ)=\sin(-60^\circ)=-\frac{\sqrt3}{2}.$
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