The standard form of a periodic model is f(x) = a sin(b⋅(x - h)) + k. On this page, we’ll explore the role of amplitude a in periodic functions. Open the Desmos File Exploring Periodic Functions. You should be on Slide 2: Modeling the Ferris Wheel Dataset (sin) and see four sliders for a, b, h, and k.
1 Adjust the sliders to fit the data as best you can, and fill in the coefficients: a, b, h and k
2 Change ONLY the slider for a, experimenting with values at 100, 50, -50, and 0, graphing each curve below. For each curve, label the coordinates at time=15, 30, and 45.
a = 100 |
a = 50 |
a = - 50 |
a = 0 |
3 What does a tell us about a periodic function?
The distance between two adjacent peaks or troughs is called the period: the interval over which the pattern repeats itself.
4 What effect does changing a have on the period of a periodic function?
These materials were developed partly through support of the National Science Foundation, (awards 1042210, 1535276, 1648684, 1738598, 2031479, and 1501927). 
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