Precalculus (10th Edition)

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

Chapter 7 - Analytic Trigonometry - Chapter Review - Review Exercises - Page 506: 48



Work Step by Step

Recall: $\sin(\alpha-\beta)=\sin(\alpha)\cos(\beta)-\cos(\alpha)\sin(\beta)$ Hence, $\sin(-\frac{\pi}{12})\\ =\sin{(-15^\circ)}\\ =\sin{(30^\circ-45^\circ)}\\ =\sin{30^\circ}\cos{45^\circ}-\cos{30^\circ}\sin{45^\circ}\\ =\frac{1}{2}\frac{\sqrt2}{2}-\frac{\sqrt3}{2}\frac{\sqrt2}{2}\\ =\frac{\sqrt2-\sqrt6}{4}$
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