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 h, experimenting with values at $$\displaystyle -58\pi \over\displaystyle 8$$, $$\displaystyle -19\pi \over\displaystyle 8$$, $$\displaystyle 19\pi \over\displaystyle 8$$, and $$\displaystyle 58\pi \over\displaystyle 8$$, graphing each curve below. For each curve, label the coordinates at time=15, 30, and 45.
$$\displaystyle h={-58\pi \over\displaystyle 8}$$ |
$$\displaystyle h={-19\pi \over\displaystyle 8}$$ |
$$\displaystyle h={19\pi \over\displaystyle 8}$$ |
$$\displaystyle h={58\pi \over\displaystyle 8}$$ |
3 Describe the change in the graph when h increases:
4 Describe the change in the graph when h decreases:
5 The model fits as long as h changes by increments of $$\displaystyle 77\pi \over\displaystyle 8$$, because
These materials were developed partly through support of the National Science Foundation, (awards 1042210, 1535276, 1648684, 1738598, 2031479, and 1501927). 
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