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: 59a

Answer

$31^{\circ}$F

Work Step by Step

Since March $15$ corresponds to Day $74$, we substitute $x=74$ in the formula: $T(74)=37+21\sin[\frac{2\pi}{365}(x-91)]$ $T(74)=37+21\sin[\frac{2\pi}{365}(74-91)]$ $T(74)=37+21\sin[\frac{2\pi}{365}(-17)]$ $T(74)=37+21\sin[-0.293]$ $T(74)=37+21(-0.289)$ $T(74)=37-6.065$ $T(74)=30.93\approx31^{\circ}$F Therefore, on Day $74$, the temperature is $31^{\circ}$F.
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