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## Q. 5.3.12

Modeling the time of sunrise

The times of sunrise in Miami, Florida, on the first of every month for one year are shown in the following table (U.S. Naval Observatory, http://aa.usno.navy.mil). The time is the number of minutes after 5 A.M.

 Month Time Month Time 1 127 7 33 2 125 8 47 3 104 9 61 4 72 10 73 5 44 11 90 6 29 12 111

Use the sinusoidal regression feature of a graphing calculator to find an equation that fits the data. Graph the data and the curve on your graphing calculator. Find the period from the equation.

## Verified Solution

Enter the data and use the sinusoidal regression feature (SinReg) to get y = 49.92 sin(0.47x + 1.42) + 81.54, where x is the month and y is the number of minutes after 5 A.M. Figure 5.59 shows the data and the sine curve. The period is 2π/0.47, or approximately 13.4 months. Since the period should be 12 months, the sine curve does not fit the data very well. See Exercises 99 and 100 for some data that really look like a sine curve.