## Trigonometry (11th Edition) Clone

Published by Pearson

# Chapter 6 - Inverse Circular Functions and Trigonometric Equations - Section 6.3 Trigonometric Equations II - 6.3 Exercises - Page 281: 62b

#### Answer

In December, the average monthly temperature in Phoenix is $55^\circ F$.

#### Work Step by Step

$$f(x)=19.5\cos[\frac{\pi}{6}(x-7)]+70.5$$ The question asks when the average monthly temperature in Phoenix is $55^\circ F$ In other words, find $x$ so that $f(x)=55$. Therefore, we can replace $f(x)=55$ to the given equation and find $x$: $$19.5\cos[\frac{\pi}{6}(x-7)]+70.5=55$$ $$19.5\cos[\frac{\pi}{6}(x-7)]=-15.5$$ $$\cos[\frac{\pi}{6}(x-7)]=-\frac{15.5}{19.5}=-\frac{31}{39}$$ $$\frac{\pi}{6}(x-7)=\cos^{-1}(-\frac{31}{39})\approx2.4896$$ $$x-7=2.4896\times\frac{6}{\pi}$$ $$x-7\approx4.7548$$ $$x=11.7548\approx12$$ $x=12$ refers to the month December. Thus, in December, the average monthly temperature in Phoenix is $55^\circ F$.

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