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: 61a


In July, the average monthly temperature is $64^\circ F$.

Work Step by Step

$$f(x)=14\sin[\frac{\pi}{6}(x-4)]+50$$ The question asks when the average temperature is $64^\circ F$ In other words, find $x$ so that $f(x)=64$. Therefore, we can replace $f(x)=64$ to the given equation and find $x$: $$14\sin[\frac{\pi}{6}(x-4)]+50=64$$ $$14\sin[\frac{\pi}{6}(x-4)]=14$$ $$\sin[\frac{\pi}{6}(x-4)]=1$$ $$\frac{\pi}{6}(x-4)=\sin^{-1}1=\frac{\pi}{2}$$ $$x-4=\frac{\pi}{2}\times\frac{6}{\pi}=3$$ $$x=7$$ $x=7$ refers to the month July. Thus, in July, the average monthly temperature is $64^\circ F$.
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