6.4 Notes

Graphing trigonometric functions

transformationally: changes to coefficient A

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

Amplitude Transformations If the coefficient of the trigonometric

function is positive one, then the graph is the parent graph.

y = sin x:

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

Amplitude Transformations If the coefficient is negative, then the parent

graph is reflected across the x-axis. For example, 80sin :y

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.

Amplitude TransformationsExample 1: cos , 2cosy y

Amplitude TransformationsExample 2:

1sec , sec

2y y

Amplitude TransformationsExample 3: tan , 3 tany y

3 50 2 3

2 2 2 2