Precalculus (6th Edition) Blitzer

Published by Pearson

Chapter 4 - Section 4.5 - Graphs of Sine and Cosine Functions - Exercise Set - Page 597: 84

Answer

See graph and explanations.

Work Step by Step

Based on the given data, we can make a graph as shown in the figure. It can be seen that the pattern resembles a sine curve $y=38+15sin(\omega t+\phi)$. As the period is $p=12$ hours, we have $\omega=\frac{2\pi}{p}=\frac{\pi}{6}$. At $t=0, y=23$, we have $sin\phi=-1$ and $\phi=-\frac{\pi}{2}$; thus $y=38+15sin(\frac{\pi}{6} t-\frac{\pi}{2})$.

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