1.
1
XINMIN SECONDARY SCHOOL
ADDITIONAL MATHEMATICS
GRAPHS OF SINE AND COSINE FUNCTIONS
WORKSHEET 1
Name: __________________________( ) Date: __________
Class: Sec 306
Sketch the graph of the following functions with the given domain.
1. y = sin x for 0° ≤ x ≤ 360°
1
0.5
0
0 60 120 180 240 300 360
-0.5
-1
2. y = cos x for 0° ≤ x ≤ 360°
1
0.5
0
0 60 120 180 240 300 360
-0.5
-1
Annie Yeo/XMS/14/07/2006
2.
2
XINMIN SECONDARY SCHOOL
ADDITIONAL MATHEMATICS
GRAPHS OF SINE AND COSINE FUNCTIONS
WORKSHEET 2
Name: _____________________________( ) Date: _________
Class: Sec 306
Note: Before typing the functions, remember to pull down ‘Zoom’ to change the scales to ‘Trig
Scales’.
1 Use the program ‘Omnigraph’ to plot the graphs of y = sin 2 x , y = sin 4 x , y = sin 2 x and
1
y = sin 4 x separately for 0° ≤ x ≤ 360° and −1.5 ≤ y ≤ 1.5 .
1
2 Refer to each of the graphs, complete the following statements.
a) The amplitude of the graph of y = sin 2 x is ____________ and its frequency is __________.
b) The amplitude of the graph of y = sin 4 x is ____________ and its frequency is __________.
c) The amplitude of the graph of y = sin 2 x is ____________ and its frequency is __________.
1
d) The amplitude of the graph of y = sin 4 x is ____________ and its frequency is __________.
1
In general, the graph of y = sin bx has amplitude of ___________ and a frequency of
__________ for 0° ≤ x ≤ 360° .
3 Use the program ‘Omnigraph’ to plot the graphs of, y = 2 sin x , y = 4 sin x , y = 1
2
sin x and
y = 2 sin x separately for 0° ≤ x ≤ 360° and −4.5 ≤ y ≤ 4.5 .
3
4 Refer to each of the graphs, complete the following statements.
a) The amplitude of the graph of y = 2 sin x is ____________ and its frequency is __________.
b) The amplitude of the graph of y = 4 sin x is ____________ and its frequency is __________.
c) The amplitude of the graph of y = 1
2
sin x is ____________ and its frequency is __________.
d) The amplitude of the graph of y = 3
2
sin x is ____________ and its frequency is __________.
In general, the graph of y = a sin x has amplitude of _______________ and a frequency of
_______________ for 0° ≤ x ≤ 360° .
Hence, the graph of y = a sin bx has amplitude of _________________ and a frequency of
______________ for 0° ≤ x ≤ 360°
Annie Yeo/XMS/14/07/2006
3.
3
5 Use the program ‘Omnigraph’ to plot the graphs of y = cos 3x , y = cos 1 x , y = cos 5x and
3
y = cos 2 x separately for 0° ≤ x ≤ 360° and −1.5 ≤ y ≤ 1.5 .
5
6 Refer to each of the graphs, complete the following statements.
a) The amplitude of the graph of y = cos 3x is ____________ and its frequency is __________.
b) The amplitude of the graph of y = cos 1 x is ____________ and its frequency is __________.
3
c) The amplitude of the graph of y = cos 5x is ____________ and its frequency is __________.
d) The amplitude of the graph of y = cos 2 x is ____________ and its frequency is __________.
5
In general, the graph of y = cos bx has amplitude of _______________ and a frequency of
_______________ for 0° ≤ x ≤ 360° .
7 Use the program ‘Omnigraph’ to plot the graphs of y = 3 cos x , y = 1
3
cos x , y = 5 cos x and
y = cos x separately for 0° ≤ x ≤ 360° and −5.5 ≤ y ≤ 5.5 .
5
2
8 Refer to each of the graphs, complete the following statements.
a) The amplitude of the graph of y = 3 cos x is ______________ and its frequency is __________.
b) The amplitude of the graph of y = 1
3
cos x is ______________ and its frequency is __________.
c) The amplitude of the graph of y = 5 cos x is ______________ and its frequency is __________.
d) The amplitude of the graph of y = 5
2
cos x is ______________ and its frequency is __________.
In general, the graph of y = a cos x has amplitude of _______________ and a frequency of
________________ for 0° ≤ x ≤ 360° .
Hence, the graph of y = a cos bx has amplitude of _________________ and a frequency of
______________ for 0° ≤ x ≤ 360°
Annie Yeo/XMS/14/07/2006
4.
4
XINMIN SECONDARY SCHOOL
ADDITIONAL MATHEMATICS
GRAPHS OF SINE AND COSINE FUNCTIONS
WORKSHEET 3
Name: _____________________________( ) Date: _________
Class: Sec 3E2
1 The graph of y = sin x for 0° ≤ x ≤ 360° is shown below. Sketch the graph of the function
y = sin 3x for 0° ≤ x ≤ 360° on the same axes:
1
0.5
0
0 60 120 180 240 300 360
-0.5
-1
y=sinx
2 Sketch the graph of the function y = 3 sin x for 0° ≤ x ≤ 360°
1
0.5
0
0 60 120 180 240 300 360
-0.5
-1
Annie Yeo/XMS/14/07/2006
5.
5
3 The graph of y = cos x for 0° ≤ x ≤ 360° is shown below. Sketch the graph of the function
y = cos 1 x for 0° ≤ x ≤ 360° on the same axes:
3
1
0.5
0
0 60 120 180 240 300 360
-0.5
-1
4 Sketch the graph of the function y = 1 cos x for 0° ≤ x ≤ 360°
2
1
0.5
0
0 60 120 180 240 300 360
-0.5
-1
Annie Yeo/XMS/14/07/2006
6.
6
5 Sketch the graph of the function y = 3 sin 2 x for 0° ≤ x ≤ 360°
1
0.5
0
0 60 120 180 240 300 360
-0.5
-1
6 Sketch the graph of the function y = 5 cos 3x for 0° ≤ x ≤ 360°
1
0.5
0
0 60 120 180 240 300 360
-0.5
-1
Annie Yeo/XMS/14/07/2006
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