Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 4 - Graphs of the Circular Functions - Section 4.1 Graphs of the Sine and Cosine Functions - 4.1 Exercises - Page 144: 44

Answer

$y=3 \cos \frac{1}{2}x$

Work Step by Step

Upon inspection, we find that the graph shows a cos function with an amplitude of 3 and a period of $4\pi$. In the standard equation $y=a \cos bx$, $a$ is the amplitude. Since the amplitude is 3, $a$ is equal to 3. To find the value of $b$, we use the formula: Step 1: Period$=\frac{2\pi}{b}$ Step 2: $4\pi=\frac{2\pi}{b}$ Step 3: $b=\frac{2\pi}{4\pi}$ Step 4: $b=\frac{1}{2}$ Substituting the values of $a$ and $b$ in the equation $y=a \cos bx$, we find that the equation of the graph is $y=3 \cos \frac{1}{2}x$.
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