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You are given a table of average monthly temperatures and a scatter plot based on the data. Use the methods of Example 8 to find a periodic function of the form $y=A \sin (B t-C)+D$ whose values approximate the monthly temperatures. The data in these exercises, as well as in Exercise $51,$ are from the Global Historical Climatology Network, and can be accessed on the Internet through the following website created by Robert Hoare.

(GRAPH CANT COPY)

Average Monthly Temperatures for Beira, Mozambique

$$\begin{array}{lc}\hline \text { Month } & \text { Temperature }\left(^{\circ} \mathrm{F}\right) \\

\hline \text { Jan. } & 81.3 \\\text { Feb. } & 81.3 \\\text { Mar. } & 80.1 \\\text { Apr. } & 77.5 \\

\text { May } & 73.0 \\\text { June } & 69.4 \\\text { July } & 68.7 \\\text { Aug. } & 70.2 \\

\text { Sept. } & 73.4 \\\text { Oct. } & 76.6 \\\text { Nov. } & 79.0 \\\text { Dec. } & 80.4 \\\hline\end{array}$$

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Oregon State University

Baylor University

Numerade Educator

University of Michigan - Ann Arbor

so looking at the daytime the table What we find is that the maximum temperature occurs in February, which is the second month, and that maximum temperature is 81.3 and the minimum temperature offers in July, which is the seventh month and that minimum temperature is 68.73 spire night. So from here we can calculate the values Bianca Cute, eh, which is maximum minus the minimum, divided by two. So that would be 81.3 minus 68.7, divided by two. So that equals 6.3. The period since the temperatures given over a year would B 12 and B is equal to two pi divided by the period. So that would be to pie divided by 12. And that's equal to pi work. Six. Next, we'll calculate the mean temperature, which would be put to D so D is equal to maximum, plus the minimum divided like to so the maximum we have is 81.3, and the minimum we have a 60 year 600.7 so at them, and then divide a sum by two that gives the value for T is equal to 80.0. Now these mean temperature first uppers in March so mean temperature first occurs in March, and we know that march is the third month off the year and also during March. So the tempter in February is higher and the temperature in April is lower. So the model would be why is equal to negative A, which is a 6.3 sign off pi over six times T minus three and then plus 80.0. Or why is equal to negative 6.3 sign off high over 16 minus piped over to plus 80.0.