Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 5 - Review Exercises - Page 707: 19


The required value is $\frac{1}{2}$

Work Step by Step

We use the identity for $\sin \left( C-D \right)$: $sin\left( C-D \right)=\sin C\text{cos }D-\cos C\sin D$. Thus, we apply the difference formula in the given expression: $\begin{align} & \sin {{80}^{\circ }}\cos {{50}^{\circ }}-\cos {{80}^{\circ }}\sin {{50}^{\circ }}=\sin \left( {{80}^{\circ }}-{{50}^{\circ }} \right) \\ & =\sin {{30}^{\circ }} \\ & =\frac{1}{2} \end{align}$
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