Precalculus (10th Edition)

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

Chapter 6 - Trigonometric Functions - 6.4 Graphs of the Sine and Cosine Functions - 6.4 Assess Your Understanding - Page 408: 22


amplitude: $\frac{9}{5}$ period: $\frac{4}{3}$

Work Step by Step

If a function has form $y=A\cos(\omega x)$, then there $|A|$ stands for the amplitude. First we identify $\omega$ and $A$ from the form of $y=A{(\cos\omega x)}$. Hence, $A=\left|\frac{9}{5}\right|=\frac{9}{5}$, $\omega=\frac{-3\pi}{2}.$ To get the period $T$ we can use the formula $T=\left|\frac{2\pi}{\omega}\right|$ to obtain $T=\left|\dfrac{2\pi}{\frac{-3\pi}{2}}\right|=\dfrac{4}{3}$
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