Precalculus (10th Edition)

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

Chapter 7 - Analytic Trigonometry - 7.7 Product-to-Sum and Sum-to-Product Formulas - 7.7 Assess Your Understanding - Page 503: 58


$|A|=5$, $T=\frac{\pi}{2}$, $\text{phase shift}=\frac{\pi}{4}$.

Work Step by Step

The general form for the cosinusoidal function is: $y=A\cos{(\omega x-\phi)}+B$ where $|A|$ is the amplitude, $B$ is the vertical shift, the period can be computed by the formula $T=\frac{2\pi}{\omega}.$ The phase shift is $\frac{\phi}{\omega}$, hence $\phi=\omega\cdot\text{phase shift}.$ Hence here: $|A|=|5|=5$, $B=0$, $\omega=4$, thus $T=\frac{2\pi}{\omega}=\frac{2\pi}{4}=\frac{\pi}{2}$, $\phi=\pi$, hence $\text{phase shift}=\frac{\phi}{\omega}=\frac{\pi}{4}$.
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