Explore the amplitude, period, and phase shift by examining the graphs of various trigonometric functions. Students can select values to use within the function to explore the resulting changes in the graph.
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Using the pull-down menus, select values for a, b, c, and d. The graph of the function will be updated automatically.
Selecting the "show base function" option causes the basic function (with a = b = 1 and c = d = 0) to be graphed in red. The function with other values for the parameters appears in green. (Note that if the parameters of the base function are the same as the values for your function, the graphs will be superimposed.)
Choose "degrees" to graph the function in degree measure, and choose "radians" to graph the function in radian measure.
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Change the values of a, b, c and d one at a time.
- What effect does changing the value of a have on the graph?
- What effect does changing the value of b have on the graph?
- What effect does changing the value of c have on the graph?
- What effect does changing the value of d have on the graph?
Given what you discovered, predict what the graph of 8 cos(2x – 30°) + 7 would look like. What are its amplitude and period?
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