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

MATHEMATICS · Multi-part · A Level · Mathematics · Trigonometry · Trigonometry

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

Related theory

Trigonometric Graphs
Trigonometric Functions
Trigonometric Modeling

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