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 1: Modeling the Ferris Wheel Dataset (sine) and see four sliders for a, b, h, and k.
1 Adjust the sliders to fit the data as best you can, then record your model settings: a, b, h and k.
2 Click on one of the peaks (highest-points) on the graph of your periodic function. Desmos will add a gray dot to all of the peaks.
3 Leaving the other sliders where they best fit the data, change ONLY the slider for b, experimenting with values at 0.2, 0.1, 0.05, and 0, graphing each curve below.
For each curve, label two adjacent peaks.
b = 0.2 |
b = 0.1 |
b = 0.05 |
b = 0 |
The distance between two adjacent peaks or valleys is called the period: the interval over which the pattern repeats itself.
4 What is the period when b = 0.2? when b = 0.1? When b = 0.5? ★ When b = 0?
5 As the frequency (b) doubles, the period . As the frequency (b) gets cut in half, the period
These materials were developed partly through support of the National Science Foundation, (awards 1042210, 1535276, 1648684, 1738598, 2031479, and 1501927). 
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