The normal daily maximum temperatures T (in degrees Fahrenheit) for a certain city are shown in the table.

Question

Month	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sept	Oct	Nov	Dec
Temperature	31.0	35.3	46.6	59.0	70.0	79.7	84.1	81.9	74.8	62.3	48.2	34.8

(a)

Use a graphing utility to plot the data and find a model for the data of the form

T(t) = a + b sin(ct − d)

where T is the temperature and t is the time in months, with t = 1 corresponding to January. (Round all numerical values to two decimal places.)

T(t)+=?

Answer 1

You can use a TI calculator. L1 get 1 to 12 L2 gets T data. You can do this by clicking STAT, then edit. Put numbers in the list hitting return after every entry. Do 2nd quit, then STAT and calc. Scroll down to sin approximation and it will give you the coefficients for the form asin(bx+c)+d . Adjust for the constants asked for in your problem - This will be the best fit to the data.