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 410: 73

Answer

$y=-4\ cos(3x)$

Work Step by Step

Step 1. As the curve is even and passes $(0,-4)$, we can write a general form $y=-A\ cos(kx)$ Step 2. We can identify the amplitude $A=4$. Step 3. We can identify the period $p=\frac{2\pi}{3}$, thus $\frac{2\pi}{k}=\frac{2\pi}{3}$ and $k=3$ Step 4. The equation is $y=-4\ cos(3x)$
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