Unit Circle Practice

Sam Shah's applet for practicing finding special angles on the unit circle and their sines and cosines

Variation on John Golden's GeoGebra Ferris Wheel

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!"

Ferris Wheel

This is a full-featured and beautifully designed GeoGebra applet from John Golden that allows students to practice fitting parameters to a cosine function which models the height of a ferris wheel car above the ground as a function of time. You can watch the ferris wheel spin as the height curve is generated and it provides an endless source of practice since you can always generate a new ferris wheel.

Spinning Out Sine and Cosine

A nice animation from the Wolfram Demonstrations Project showing the relationship between a circle and the graphs of sine and cosine. I like the way the cosine graph is show on its side. I'm going to try using it (after editing it in Mathematica to remove the sine and cosine labels) as an introduction both to the unit circle and the trig graphs. It looks like a good candidate for the technique of showing an animation with no commentary and then asking for student questions, writing them on the board, and asking for answers to/discussion of any of the questions.

Modeling with sine and cosine

In this applet, you look at the graph of a data set (for water level in Cape May, NJ on October 13, 2009) and try to fit a sine function and a cosine function to the data. You can type in your function to see how well it fits the data. Some instruction on how to determine the parameters is provided.

Writing Equations for Sine and Cosine Functions

This applet I created with GeoGebra has 40 problems, which get progressively more difficult, in which the student must write an equation for a graph which is a stretch and/or translation of a sine/cosine graph. To check whether an equation is correct, the student types in the equation and looks at whether the graphs match up.

Introduction to the Unit Circle

These are three versions of an applet that I created using GeoGebra to introduce students to the unit circle. One version presents the idea in terms of distance traveled around the circle. The other two present the idea in terms of the measure of the central angle. There is a radian version and a degree version.