Trigonometry (10th Edition)

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

Chapter 4 - Review Exercises - Page 184: 46



Work Step by Step

The y-values vary from $−0.5$ to $0.5$. This means that the amplitude: $\frac{0.5-(-0.5)}{2}=\frac{1}{2}=0.5$. The given graph looks like a cosine function with no reflection about the x-axis. This means that the value of $a$ is positive. Since the amplitude is $|a|$ and is known to be $0.5$, then $a=0.5$. Thus, the tentative equation of the function whose graph is given is $y=0.5\cos(bx)$. The period of the cosine function is $\frac{2\pi}{b}$. The given graph clearly shows that the period of the function is $\pi$. Thus, $\frac{2\pi}{b}=\pi \\2\pi=b{\pi} \\\frac{2\pi}{\pi}=\frac{b{\pi}}{\pi} \\2=b$ Therefore, the equation of the function whose graph is given is $\color{blue}{y=0.5\cos(2x)}$.
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