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- 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 = sin x for 0° ≤ x ≤ 360° 2 1 0 0 60 120 180 240 300 360 -1 2 2. y = cos x for 0° ≤ x ≤ 360° 2 1 0 0 60 120 180 240 300 360 -1 2 Annie Yeo/XMS/03/08/2010
- 2. 2 3. y = tan x for 0° ≤ x ≤ 360° 10 5 0 0 60 120 180 240 300 360 -5 -10 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 2x is ________ and its frequency is _________. (b) The amplitude of the graph of y = sin 4x 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 . Annie Yeo/XMS/03/08/2010
- 4. 4 4 Refer to each of the graphs, complete the following statements. (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 3x 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 y = sin 3 x 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 = 3sin x for 0° ≤ x ≤ 360° . 4 2 0 0 60 120 180 240 300 360 -2 -4 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 y = cos x for 0° ≤ x ≤ 360° on the same axes: 3 1 0.5 0 0 60 120 180 240 300 360 -0.5 -1 1 4 Sketch the graph of the function y = cos x for 0° ≤ x ≤ 360° . 2 1 0.5 0 0 60 120 180 240 300 360 -0.5 -1 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: 6 4 asymptote asymptote 2 0 0 60 120 180 240 300 360 -2 -4 -6 -8 y=tanx 1 6 Sketch the graph of the function y = tan x for 0° ≤ x ≤ 360° . 3 6 4 2 0 0 60 120 180 240 300 360 -2 -4 -6 Annie Yeo/XMS/03/08/2010
- 10. 10 7 Sketch the graph of the function y = −3sin 2 x for 0° ≤ x ≤ 360° . 4 2 0 0 60 120 180 240 300 360 -2 -4 8 Sketch the graph of the function y = 5cos 3x for 0° ≤ x ≤ 360° . 6 4 2 0 0 60 120 180 240 300 360 -2 -4 6 Annie Yeo/XMS/03/08/2010

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