Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 7 - Trigonometric Identities and Equations - 7.3 Sum and Difference Identities - 7.3 Exercises - Page 679: 41


$\dfrac {\sqrt {2}}{4}\left( \sqrt {3}-1\right) $

Work Step by Step

$\sin {165}=\sin \left( 120+45\right) =\sin {120}\cos 45+\cos {120}\sin 45=\dfrac {\sqrt {3}}{2}\times \dfrac {\sqrt {2}}{2}-\dfrac {1}{2}\dfrac {\sqrt {2}}{2}=\dfrac {\sqrt {2}}{4}\left( \sqrt {3}-1\right) $
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