I love John Golden's GeoGebra Ferris Wheel, which he's written about here and I've written about here. I also love how GeoGebraTube makes it so easy to start with the great work of someone else and create a variation on it. Here's my variation on John's creation for a user who's slightly more experienced with transformations and with sine and cosine functions. Rather than asking the user to come up with parameters for a given function, it requires the user to come up with the whole function. I also added the option to hide the actual function so that the user could begin by thinking about what it would look like.We had a great discussion in precalculus class today based on a single randomly generated wheel. We went wherever student questions and answers took us and ended up covering lots of ground. The particularly interesting stuff from my perspective came when those who saw the graph as a shifted sine wave were fighting it out with those who saw it as a shifted cosine wave and those who saw it as a flipped cosine wave. Finally lots of people were seeing lots of ways that they might write an equation for a sinusoidal wave. At the very end of class we generated a new wheel and everyone tried to write a function to go along with it. Class was over and people were pleading, "Please--try my equation!"
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