Here’s a table of average monthly temperatures at Wellington Airport. Each data point was obtained by averaging over the years from 1971–2000.

a. Graph these data. (Time should be in units of months, with t = 0 corresponding to 1 Jan).

b. How would you describe these data using a cos function?
How about using a sin function?
Hint: to use a trig function to describe the data you need to estimate the period, amplitude, and horizontal and vertical offsets.

c. What differences would you expect to see if these temperatures were measured from a place in the northern hemisphere, and how would you alter the sin and cos functions to compensate?

d. Check your answer from the previous part by going to this web site, and selecting two cities, one in the northern hemisphere, one in the southern. For each location go to the "Climate(Averages)" tab and make a table of the average monthly maximum temperature. Plot your function, and fit with a trig function. Compare your two cities.