6.4 Notes Graphing trigonometric functions transformationally: changes to coefficient A.
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Transcript of 6.4 Notes Graphing trigonometric functions transformationally: changes to coefficient A.
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6.4 Notes
Graphing trigonometric functions
transformationally: changes to coefficient A
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Amplitude TransformationsTo make a change to the amplitude of the graph of a trigonometric function, modify the coefficient, A, of the trigonometric equation.
trigy A B C D
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Amplitude Transformations If the coefficient of the trigonometric
function is positive one, then the graph is the parent graph.
y = sin x:
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Amplitude Transformations A coefficient with an absolute value
greater than 1 increases the amplitude. The graph is taller than the parent graph.
A coefficient with an absolute value less than 1 decreases the amplitude. The graph is shorter than the parent graph.
http://id.mind.net/~zona/mstm/physics/waves/introduction/introductionWaves.html
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Amplitude Transformations If the coefficient is negative, then the parent
graph is reflected across the x-axis. For example, 80sin :y
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Amplitude TransformationsFor the following example problems and for the homework, the directions are to graph the pair of functions on the same graph using conventional graphing techniques.
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Amplitude TransformationsExample 1: cos , 2cosy y
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Amplitude TransformationsExample 2:
1sec , sec
2y y
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Amplitude TransformationsExample 3: tan , 3 tany y
3 50 2 3
2 2 2 2