## Trigonometry (11th Edition) Clone

In October, the average monthly temperature in Phoenix is $70.5^\circ F$.
$$f(x)=19.5\cos[\frac{\pi}{6}(x-7)]+70.5$$ The question asks when the average monthly temperature in Phoenix is $70.5^\circ F$ In other words, find $x$ so that $f(x)=70.5$. Therefore, we can replace $f(x)=70.5$ to the given equation and find $x$: $$19.5\cos[\frac{\pi}{6}(x-7)]+70.5=70.5$$ $$19.5\cos[\frac{\pi}{6}(x-7)]=0$$ $$\cos[\frac{\pi}{6}(x-7)]=0$$ $$\frac{\pi}{6}(x-7)=\cos^{-1}0=\frac{\pi}{2}$$ $$x-7=\frac{\pi}{2}\times\frac{6}{\pi}$$ $$x-7=3$$ $$x=10$$ $x=10$ refers to the month October. Thus, in October, the average monthly temperature in Phoenix is $70.5^\circ F$.