At the Mawson Base in Antarctica

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

Problem

At the Mawson Base in Antarctica, the mean monthly temperatures for the last 30 years are:

Month	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec
Temperature ( $^\circ\text{C}$ )	$0$	$0$	$-4$	$-9$	$-14$	$-17$	$-18$	$-19$	$-17$	$-13$	$-6$	$-2$

(1) Find a sine model for this data without using technology. Use Jan

\equiv1

, Feb

\equiv2

, and so on. (2) Draw a scatter diagram of the data and sketch the graph of your model on the same set of axes. (3) How appropriate is the model?