Cambridge Additional Mathematics

228 Trigonometric functions (Chapter 9)

TERMINOLOGY USED TO DESCRIBE PERIODICITY

Aperiodic functionis one which repeats itself over and over in

a horizontal direction, in intervals of the same length.

Theperiodof a periodic function is the length of one repetition

or cycle.

f(x)is a periodic function with periodp,f(x+p)=f(x)

for allx, andpis the smallest positive value for this to be true.

Acycloidis an example of a periodic function. It is the curve traced out by a point on a circle as the circle

rolls across a flat surface in a straight line.

Use agraphing packageto examine the function f(x)=x¡[x]

where [x] is “the largest integer less than or equal tox”.

Isf(x)periodic? What is its period?

WAVES

In this course we are mainly concerned with periodic phenomena which show a wave pattern.

The wave oscillates about a horizontal line called theprincipal axisormean linewhich has

equation y=

max+min

2

.

Amaximum pointoccurs at the top of a crest, and aminimum pointat the bottom of a trough.

Theamplitudeis the distance between a maximum (or minimum) point and the principal axis.

amplitude=

max¡min

2

,means

“if and only if ”.___

GRAPHING

PACKAGE

DEMO

horizontal flat surface

amplitude

minimum point

maximum point

principal axis

period

cyan magenta yellow black

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Additional Mathematics
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