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# Worksheets on graphs of trigonometry

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### Worksheets on graphs of trigonometry

1. 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. 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. 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. 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. 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. 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