Part 2: Model real-world problems using sinusoids. 1. The average monthly high temperatures for Phoenix, Arizona from the years 1981-2010 are shown in the table below, with the value 1 representing the month of January, and the value of 12 representing the month of December. Complete the following steps to model the curve using the sine function.

Month Average Temperature (°F)
1 69
2 72
3 78
4 86
5 95
6 104
7 106
8 104
9 100
10 89
11 76
12 67

a) Make a scatterplot of the data. Use the grid below or include a screenshot of the data plotted from a calculator. (2 points)

b) What is the minimum temperature in the data set? (1 point)

c) What is the maximum temperature in the data set? (1 point)

d) What is the vertical shift, k, for the data set? (2 points)

e) What is the amplitude, a, for the data set? (2 points)

f) What is the period and frequency factor for the data set? (2 points)

g) What is the phase shift for the data set? (2 points)

h) Write an equation using the sine function that models this data set. (5 points)

i) When would you expect the temperature in Phoenix to be 82°? (2 points)