Below is a table showing the mean monthly maximum temperatures for a city in Greece

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

Problem

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

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

(1) Draw a scatter diagram of the data. (2) What features of the data suggest a trigonometric model is appropriate? (3) Model the data with a sine function of the form

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

, where

\text{Jan}\equiv1

\text{Feb}\equiv2

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

b

, (ii)

a

, (iii)

d

, and (iv)

c

. (4) Use technology to check your model. How well does your model fit?

Related theory

Trigonometric Modeling
Trigonometric Functions

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