Problem

Below is a table which shows the mean monthly maximum temperatures for a city in Greece.

Month	Jan	Feb	Mar	Apr	May	Jun	July	Aug	Sept	Oct	Nov	Dec
Temperature ( $^{\circ}\text{C}$ )	15	14	15	18	21	25	27	26	24	20	18	16

a. Draw a scatter diagram of the data. b. What features of the data suggest a trigonometric model is appropriate? c. Your task is to model the data with a sine function of the form

T \approx a \sin(b(t - c)) + d

, where

\text{Jan} \equiv 1

\text{Feb} \equiv 2

, and so on. Without using technology, estimate: i

b

a

iii

d

c

d. Use technology to check your model. How well does your model fit?

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