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: 45

Answer

$y=3 \sin 4x$

Work Step by Step

Upon inspection, we find that the graph shows a sin function with an amplitude of 3 and a period of $\frac{\pi}{2}$. In the standard equation $y=a \sin bx$, $a$ 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: $\frac{\pi}{2}=\frac{2\pi}{b}$ Step 3: $b=\frac{2\pi}{\frac{\pi}{2}}$ Step 4: $b=4$ Substituting the values of $a$ and $b$ in the equation $y=a \sin bx$, we find that the equation of the graph is $y=3 \sin 4x$.
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