Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 5 - Section 5.5 - Trigonometric Equations - Exercise Set - Page 705: 132


$ 109$ and $ 231$ days after Jan. 1st.

Work Step by Step

Step 1. Given the model function $y=3\ sin[\frac{2\pi}{365}(x-79)]+12$ at $y=13.5\ hours$, we have $3\ sin[\frac{2\pi}{365}(x-79)]+12=13.5$ or $sin[\frac{2\pi}{365}(x-79)]=0.5$ Step 2. The general solutions for the above equation are $\frac{2\pi}{365}(x-79)=2k\pi+\frac{\pi}{6}$ and $\frac{2\pi}{365}(x-79)=2k\pi+\frac{5\pi}{6}$ or $x=365k+\frac{365}{12}+79$ and $x=365k+\frac{1825}{12}+79$ where $k$ is an integer. Step 3. Within a year of $x\in[0,365)$ days, we have $x\approx109$ and $x\approx231$ days after Jan. 1st.
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