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 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 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 troughs 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). 
Bootstrap by the Bootstrap Community is licensed under a Creative Commons 4.0 Unported License. This license does not grant permission to run training or professional development. Offering training or professional development with materials substantially derived from Bootstrap must be approved in writing by a Bootstrap Director. Permissions beyond the scope of this license, such as to run training, may be available by contacting contact@BootstrapWorld.org.