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.

Rational Function Graphs

Use this demonstration from the Wolfram Demonstrations Project to explore the graphs of rational functions. Predict whether the function will have any holes and then check "show holes" to see if you're right. (To interact with it online you'll need to download and install Wolfram's free CDF Player.)

Velocity of a Falling Object

Use this demonstration from the Wolfram Demonstrations Project to explore average and instantaneous velocity for a falling object. (To interact with it online you'll need to download and install Wolfram's free CDF Player.)

Graphs of Taylor Polynomials

Use this demonstration from the Wolfram Demonstrations Project to explore Taylor polynomial approximations to a variety of functions. (To interact with it online you'll need to download and install Wolfram's free CDF Player.)

Polar and Rectangular Coordinates

Use this demonstration from the Wolfram Demonstrations Project to explore the relationship between polar and rectangular coordinates. (To interact with it online you'll need to download and install Wolfram's free CDF Player.)

Max-Min Demonstrations from the Wolfram Demonstrations Project

These are some of the demonstrations from the Wolfram Demonstrations Project that illustrate classic Calculus I optimization problems. To interact with these online you'll need to download and install Wolfram's free CDF Player.