Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 4 - Quiz (Sections 4.1-4.2) - Page 164: 12

Answer

$\text{Lowest average monthly temperature }\approx 60.02^o \text{ F}$ $\text{Highest average monthly temperature }\approx 83.98^o \text{ F}$

Work Step by Step

Graph the given function usng a graphing tool to obtain the graph below. Notice that the average temperature is lowest during the month of January (where $x=1$) and highest during the month of July. (where $x=7$). Thus, \begin{align*} \text{Lowest average monthly temperature} &= 12 \cdot \sin{\left[\frac{\pi}{6}(1-3.9)\right]}+72\\ &\approx 60.02^o \text{F} \end{align*} \begin{align*} \text{Highest average monthly temperature} &= 12 \cdot \sin{\left[\frac{\pi}{6}(7-3.9)\right]}+72\\ &\approx 83.98^o \text{F} \end{align*}
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