Precalculus (6th Edition) Blitzer

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

Chapter 4 - Section 4.4 - Trigonometric Functions of Any Angle - Exercise Set - Page 576: 88

Answer

The exact value of the expression is $\frac{\sqrt{2}+1}{2}$.

Work Step by Step

Let us consider the following equation. $x=\sin \frac{\pi }{4}\cos 0-\sin \frac{\pi }{6}\cos \pi $. Put $\frac{\sqrt{2}}{2}$ for $\sin \frac{\pi }{4}$ , $1$ for $\cos 0$ , $\frac{1}{2}$ for $\sin \frac{\pi }{6}$ and $-1$ for $\cos \pi $. $\begin{align} & x=\frac{\sqrt{2}}{2}\left( 1 \right)-\left( \frac{1}{2} \right)\left( -1 \right) \\ & =\frac{\sqrt{2}}{2}+\frac{1}{2} \\ & =\frac{\sqrt{2}+1}{2} \end{align}$
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