Trigonometry (11th Edition) Clone

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

Chapter 6 - Inverse Circular Functions and Trigonometric Equations - Section 6.3 Trigonometric Equations II - 6.3 Exercises - Page 281: 61b


In February, the average monthly temperature is $39^\circ F$.

Work Step by Step

$$f(x)=14\sin[\frac{\pi}{6}(x-4)]+50$$ The question asks when the average temperature is $39^\circ F$ In other words, find $x$ so that $f(x)=39$. Therefore, we can replace $f(x)=39$ to the given equation and find $x$: $$14\sin[\frac{\pi}{6}(x-4)]+50=39$$ $$14\sin[\frac{\pi}{6}(x-4)]=-11$$ $$\sin[\frac{\pi}{6}(x-4)]=-\frac{11}{14}$$ $$\frac{\pi}{6}(x-4)=\sin^{-1}(-\frac{11}{14})\approx-0.9038$$ $$x-4=(-0.9038)\times\frac{6}{\pi}$$ $$x-4\approx-1.7262$$ $$x\approx2.2738\approx2$$ $x=2$ refers to the month February. Thus, in February, the average monthly temperature is $39^\circ F$.
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