Answer:
- 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]
Now, we apply the inverse cosine, on both sides of the equation, to find the value of m.
[tex]\cos^{-1}{\cos{(\frac{\pi}{6})(m-6)}} = \cos^{-1}{\frac{10}{27}}[/tex]
Now, with the help of a calculator, in radians:
[tex]\frac{\pi}{6}(m-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, since 8.27 + 1 = 9.28, it happens during the month of September.
