Trigonometry (11th Edition) Clone

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

Chapter 4 - Graphs of the Circular Functions - Section 4.1 Graphs of the Sine and Cosine Functions - 4.1 Exercises - Page 152: 57a



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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