Mathematics

Problem

The data in the table shows the mean monthly temperatures for Christchurch, New Zealand.

Month	Jan	Feb	Mar	Apr	May	Jun	July	Aug	Sept	Oct	Nov	Dec
Temperature ( $^{\circ}\text{C}$ )	15	16	$14\frac{1}{2}$	12	10	$7\frac{1}{2}$	7	$7\frac{1}{2}$	$8\frac{1}{2}$	$10\frac{1}{2}$	$12\frac{1}{2}$	14

a. a Find a cosine model for this data in the form

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

without using technology. Let Jan

\equiv 1

, Feb

\equiv 2

, and so on. b. b Draw a scatter diagram of the data and sketch the graph of your model on the same set of axes. c. c Use technology to check your answer to a.

Browse the problem library