1. 1
XINMIN SECONDARY SCHOOL
ADDITIONAL MATHEMATICS
GRAPHS OF SINE AND COSINE FUNCTIONS
WORKSHEET 1
Name: __________________________( ) Date: __________
Class: Sec _______
Sketch the graph of the following functions with the given domain.
1. y = 3 x for 0° ≤ x ≤ 360°
sin
2
1
0
-60 0 60 120 180 240 300 360 420
-1
-2
3
2. y = cos x for 0° ≤ x ≤ 360°
-3
2
1
0
-60 0 60 120 180 240 300 360 420
-1
-2
-3
Annie Yeo/XMS/03/08/2010

2. 2
3. y = tan x for 0° ≤ x ≤ 360°
10
5
0
-60 0 60 120 180 240 300 360 420
-5
-10
-15
Annie Yeo/XMS/03/08/2010

3. 3
XINMIN SECONDARY SCHOOL
ADDITIONAL MATHEMATICS
GRAPHS OF SINE, COSINE and TANGENT FUNCTIONS
WORKSHEET 2
Name: _____________________________( ) Date: _________
Class: Sec _______
 Log into ACE Learning Platform
 Sec 3 Express Additional Mathematics Section,
 Chapter T3 W7: Graphs and Properties of sinx, cosx and tanx
 Topic: Graphs of Trigonometric Functions
 Interactive Labs:
• Graphs of y = a cos bx + c
• Graphs of y = a sin bx + c
• Graphs of y = a tan bx + c
•
1 1
1 View the graphs of y = sin 2 x , y = sin 4 x , y = sin x and y = sin x separately for
2 4
0° ≤ x ≤ 360° and −1.5 ≤ y ≤ 1.5 .
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 __________.
1
(c) The amplitude of the graph of y = sin x is ________ and its frequency is _________.
2
1
(d) The amplitude of the graph of y = sin x is ________ and its frequency is _________.
4
In general, the graph of y = sin bx has an amplitude of ______, a frequency of ________ and
a period of ___________ for 0° ≤ x ≤ 360° .
1 3
3 View the graphs of y = 2sin x , y = 4sin x , y = sin x and y = sin x separately for
2 2
0° ≤ x ≤ 360° and −5 ≤ y ≤ 5 .
4 Refer to each of the graphs, complete the following statements.
Annie Yeo/XMS/03/08/2010

4. 4
(a) The amplitude of the graph of y = 2sin x is ________ and its frequency is _________.
(b) The amplitude of the graph of y = 4sin x is _______ and its frequency is ________.
1
(c) The amplitude of the graph of y = sin x is ________ and its frequency is _______.
2
3
(d) The amplitude of the graph of y = sin x is ________ and its frequency is ________.
2
In general, the graph of y = a sin x has an amplitude of ______, a frequency of _____ and a
period of ________ for 0° ≤ x ≤ 360° .
Hence, the graph of y = a sin bx has an amplitude of ______, a frequency of _____ and a
period of ________ for 0° ≤ x ≤ 360° .
1 5
5 View the graphs of y = cos 3 x , y = cos x , y = cos 5 x and y = cos x separately for
3 2
0° ≤ x ≤ 360° and −1.5 ≤ y ≤ 1.5 .
6 Refer to each of the graphs, complete the following statements.
(a) The amplitude of the graph of y = cos 3 x is _______ and its frequency is ________.
1
(b) The amplitude of the graph of y = cos x is _______ and its frequency is ________.
3
(c) The amplitude of the graph of y = cos 5 x is ________ and its frequency is _______.
5
(d) The amplitude of the graph of y = cos x is ________ and its frequency is _______.
2
In general, the graph of y = cos bx has an amplitude of _____, a frequency of ____ and a
period of ________ for 0° ≤ x ≤ 360° .
Annie Yeo/XMS/03/08/2010

5. 5
1 5
7 View the graphs of y = 3cos x , y = cos x , y = 5cos x and y = cos x separately for
3 2
0° ≤ x ≤ 360° and −5.5 ≤ y ≤ 5.5 .
8 Refer to each of the graphs, complete the following statements.
(a) The amplitude of the graph of y = 3cos x is ________ and its frequency is _______.
1
(b) The amplitude of the graph of y = cos x is _______ and its frequency is _______.
3
(c) The amplitude of the graph of y = 5cos x is ________ and its frequency is _______.
5
(d) The amplitude of the graph of y = cos x is _______ and its frequency is _______.
2
In general, the graph of y = a cos x has an amplitude of _____, a frequency of ____ and a
period of _____ for 0° ≤ x ≤ 360° .
Hence, the graph of y = a cos bx has an amplitude of _____, a frequency of ______ and a
period of ________ for 0° ≤ x ≤ 360°
1 5
9 View the graphs of y = tan 3x , y = tan x , y = tan 5 x and y = tan x separately for
3 2
0° ≤ x ≤ 360° and −1.5 ≤ y ≤ 1.5 .
10 Refer to each of the graphs, complete the following statements.
(a) The amplitude of the graph of y = tan 3x is __________ and its frequency is ________.
1
(b) The amplitude of the graph of y = tan x is __________ and its frequency is _______.
3
(c) The amplitude of the graph of y = tan 5 x is __________ and its frequency is _______.
5
(d) The amplitude of the graph of y = tan x is __________ and its frequency is _______.
2
In general, the graph of y = tan bx has an ___________ amplitude, a frequency of ____ and a
period of ________ for 0° ≤ x ≤ 360° .
Annie Yeo/XMS/03/08/2010

6. 6
1 5
11 View the graphs of y = 3 tan x , y = tan x , y = 5 tan x and y = tan x separately for
3 2
0° ≤ x ≤ 360° and −5.5 ≤ y ≤ 5.5 .
12 Refer to each of the graphs, complete the following statements.
(a) The amplitude of the graph of y = 3 tan x is ___________ and its frequency is _______.
1
(b) The amplitude of the graph of y = tan x is __________ and its frequency is _______.
3
(c) The amplitude of the graph of y = 5 tan x is ___________ and its frequency is _______.
5
(d) The amplitude of the graph of y = tan x is ___________ and its frequency is ______.
2
In general, the graph of y = a tanx has an __________ amplitude, a frequency of _____ and a
period of _____ for 0° ≤ x ≤ 360° .
Hence, the graph of y = a tanbx has an ___________amplitude, a frequency of ______ and a
period of ________ for 0° ≤ x ≤ 360° .
Annie Yeo/XMS/03/08/2010

7. 7
XINMIN SECONDARY SCHOOL
ADDITIONAL MATHEMATICS
GRAPHS OF SINE AND COSINE FUNCTIONS
WORKSHEET 3
Name: _____________________________( ) Date: _________
Class: Sec _______
1 The graph of y = sin x for 0° ≤ x ≤ 360° is shown below. Sketch the graph of the function
1.5
y = sin 3 x for 0° ≤ x ≤ 360° on the same axes:
1
0.5
0
-60 0 60 120 180 240 300 360 420
-0.5
-1
y=sinx
2 Sketch the graph of the function y = 3sin x for 0° ≤ x ≤ 360° .
-1.5
6
4
2
0
-60 0 60 120 180 240 300 360 420
-2
-4
-6
Annie Yeo/XMS/03/08/2010

8. 8
3 The graph of y = cos x for 0° ≤ x ≤ 360° is shown below. Sketch the graph of the function
1.5
1
y = cos x for 0° ≤ x ≤ 360° on the same axes:
3
1
0.5
0
-60 0 60 120 180 240 300 360 420
-0.5
-1
y=cosx
1
4 Sketch the graph of the function y = cos x for 0° ≤ x ≤ 360° .
1.5
-1.5
2
1
0.5
0
-60 0 60 120 180 240 300 360 420
-0.5
-1
-1.5
Annie Yeo/XMS/03/08/2010

9. 9
5 The graph of y = tan x for 0° ≤ x ≤ 360° is shown below. Sketch the graph of the function
y = tan 2 x for 0° ≤ x ≤ 360° on the same axes:
8
6
4 asymptote asymptote
2
0
-60 0 60 120 180 240 300 360 420
-2
-4
-6
-8
y=tanx
-10
x=90
Vertical line through ( 2701 ,0 )
6 Sketch the graph of the function y = tan x for 0° ≤ x ≤ 360° .
3
8
6
4
2
0
-60 0 60 120 180 240 300 360 420
-2
-4
-6
-8
7 Sketch the graph of the function y = −3sin 2 x for 0° ≤ x ≤ 360° .
Annie Yeo/XMS/03/08/2010

10. 10
6
4
2
0
-60 0 60 120 180 240 300 360 420
-2
-4
8 -6
Sketch the graph of the function y = 5cos 3 x for 0° ≤ x ≤ 360° .
8
6
4
2
0
-60 0 60 120 180 240 300 360 420
-2
-4
-6
-8
Annie Yeo/XMS/03/08/2010