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 147: 59e

Answer

$37^{\circ}$F

Work Step by Step

Since October $1$ represents Day $274$, we substitute $x=274$ in the formula: $T(274)=37+21\sin[\frac{2\pi}{365}(x-91)]$ $T(274)=37+21\sin[\frac{2\pi}{365}(274-91)]$ $T(274)=37+21\sin[\frac{2\pi}{365}(183)]$ $T(274)=37+21\sin[3.150]$ $T(274)=37+21(-0.0084)$ $T(274)=37-0.177$ $T(274)=36.82\approx37^{\circ}$F Therefore, on Day $274$, the temperature is $37^{\circ}$F.
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