Tim would like to compare the climate of Sydney Australia to

Tim would like to compare the climate of Sydney. Australia. to the climates of the other 3 cities. He collects data for the day of the year t and the average daily high temperature H in degrees Fahrenheit. As before, t = 0 represents January 1, and t = 364 represents December 31. Use your graphing calculator to perform a sinusoidal regression on the data. Write the function in the form a sig (bt + c)+ d. Round of a and d to 2 decimal places , and b and c to 4 decimal places. Circle the letters(s) of all statements that would accurately describe the climate of Sydney in comparison to the other cities. Remember that summer in the Southern Hemisphere is the months of December. January, and February. Similar temperature to Buenos Aires, but hotter in the summer. Similar temperature to Buenos Aires, but cooler in the summer. Cooler than Osaka, but more variable. About as variable as Los Angeles, but generally cooler. Warmer than Los Angeles, but not as variable. none of these What if Sydney\'s climate were equally as variable as Osaka\'s? Rew ntc the function for Sydney to account for this new variability, and complete the missing values in the table Give temperatures to the nearest tenth of a degree.

Solution

31)

Sydney climate is equally variable as Osaka

So the maximum and minimum variation of temperature for Sydeny shall be same as of Osaka.

So we make the the amplitude of sin function of Sydney(20.71) , same as of Osaka and vertical shifting of Sydney same as of Osaka( +68.97)

H(t) = 20.71 sin (.0172t + 89.7420) + 68.97

Now plugging t = 15

H(t) = 20.71 sin ( .0172*15 + 89.7420) + 68.97

H = 90 degrees

for t = 74

H(t) = 20.71 sin ( .0172*74 + 89.7420) + 68.97

H = 90 degrees

for t = 135

H(t) = 20.71 sin ( .0172*135 + 89.7420) + 68.97

H = 89.60 degrees

for t = 196

H(t) = 20.71 sin ( .0172*196 + 89.7420) + 68.97

H = 89.60 degrees

for t = 258

H(t) = 20.71 sin ( .0172*258 + 89.7420) + 68.97

H = 89.60 degrees