Cambridge Additional Mathematics

Trigonometric functions (Chapter 9) 227

On the scatter diagram alongside we plot the

temperature T on the vertical axis. We assign

October as t=1month, November as t=2

months, and so on for the rest of the year.

The cycle will approximately repeat itself for each subsequent 12 month period. By the end of the chapter

we will be able to establish aperiodic functionwhich approximately fits this set of points.

Historical note

In 1831 Michael Faradaydiscovered that an electric current was generated by rotating a coil of wire

in a magnetic field. The electric current produced showed a voltage which varied between positive and

negative values as the coil rotated through 360 ±.

GATHERING PERIODIC DATA

Data on a number of periodic phenomena can be found online or in other publications. For example:

² Maximum and minimum monthly temperatures can be found at http://www.weatherbase.com

² Tidal details can be obtained from daily newspapers or internet sites such as

http://tidesandcurrents.noaa.gov or http://www.bom.gov.au/oceanography

10

20

30

T()°C

t(months)

OCT

O

OCT

(1 21 ), Qw

36912

10

20

30

T()°C

t(months)

O

OCT OCT

3 6 9 12 15 18 21 24

OCT

lines of

magnetic

force

direction

of rotation

voltage

+

O 90° 180° 270° 360°

Graphs with this basic shape, where the cycle is repeated over and over, are calledsine waves.

4037 Cambridge

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Y:\HAESE\CAM4037\CamAdd_09\227CamAdd_09.cdr Tuesday, 7 January 2014 9:44:13 AM BRIAN