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1. 1
BUM1113 Technical Mathematics Dr Norazaliza Mohd Jamil September 2018
Chapter 5: Graphs of the Trigonometric Functions
5.1 Trigonometric Functions: periods
 Periodic function: the graphs display patterns that repeat themselves at regular intervals.
 A function f is said to be periodic if there is a number 0
p  such that
( ) ( )
f x p f x
  .
The smallest such number p is called the period of f .
 Examples of periodic function:
sin( 2 ) sin
x x

 
cos( 2 ) cos
x x

 
 The period represents the minimum number of units that we must travel along the horizontal axis before the graph begins to repeat itself.
 Let f be a periodic function and let m an M denote the minimum and maximum values of the function. Then, the amplitude of f is the
number
2
M m
A

 .
 Amplitude is always positive.
 For a function in which the graph is cantered about the horizontal axis, the amplitude is simply the maximum height of the graph above
the horizontal axis.

2. 2
BUM1113 Technical Mathematics Dr Norazaliza Mohd Jamil September 2018
Example
Specify the period and amplitude.
Period = 2
Amplitude:
4 ( 4)
4
2
A
 
 
1. 2. 3.
Example
Specify the period and amplitude.
Period 6

Amplitude:
4 2
1
2
A

 
4. 5. 6.

3. 3
BUM1113 Technical Mathematics Dr Norazaliza Mohd Jamil September 2018
Exercises 5.1:
1. Specify the period and amplitude for each function.
(a)
(b)
(c)
(d)

4. 4
BUM1113 Technical Mathematics Dr Norazaliza Mohd Jamil September 2018
(e)
(f)
(g)