Answer:
During the month of September.
Step-by-step explanation:
The temperature in Beijing, in m months after January, is given by the following equation:
[tex]T(m) = 27\cos{(\frac{\pi}{6}(m-6))} + 45[/tex]
In which m is the number of months after January.
During which month in the year would the temperature reach 55°F?
We have to find m for which: T(m) = 55. So
[tex]T(m) = 27\cos{(\frac{\pi}{6}(m-6))} + 45[/tex]
[tex]55 = 27\cos{(\frac{\pi}{6}(m-6))} + 45[/tex]
[tex]27\cos{(\frac{\pi}{6}(m-6))} = 10[/tex]
[tex]\cos{(\frac{\pi}{6}(m-6))} = \frac{10}{27}[/tex]
Applying the inverse cosine to both sides:
[tex]\cos^{-1}{(\cos{(\frac{\pi}{6}(m-6))})} = \cos^{-1}{(\frac{10}{27})}[/tex]
[tex]\frac{\pi}{6}(m-6) = 1.19[/tex]
[tex]\pi(m-6) = 6*1.19[/tex]
[tex]\pi m - 6\pi = 6*1.19[/tex]
[tex]\pi m = 6*1.19 + 6\pi[/tex]
[tex]m = \frac{6*1.19 + 6\pi}{\pi}[/tex]
[tex]m = 8.27[/tex]
8.27 months after January
8.27 + 1 = 9.27, so during the month of September.
