## Trigonometry (11th Edition) Clone

In February, the average monthly temperature is $39^\circ F$.
$$f(x)=14\sin[\frac{\pi}{6}(x-4)]+50$$ 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 $39^\circ F$.