Visualizing the dot product

Mystery Vector Function is a GeoGebra applet I created to introduce students to the dot product. In this applet, students observe a rectangle in which the length of one side is equal to the magnitude of vector b and the length of other side is equal to the projection of vector a onto b. They discover that the signed area of this rectangle is equal to the product of the magnitude of a, the magnitude of b, and the cosine of the angle between them. They can then use the angle difference identity for cosine to show that this is equal to the sum of the product of the x-components and the product of the y-components.

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.

Finding the equation of a parabola

This is an applet I created using Geogebra in which the user is asked to enter the equation of randomly generated parabola. The equation entered is graphed for comparison to the target parabola.

Blank Axes for Trig Graphs

Blank axes designed to make it easy to create standard trig graphs for insertion into word processing documents. The full power of Geogebra is behind it. To copy the graph you've made, choose "Graphics View to Clipboard" from the Edit menu.

Square Grid in Geogebra

This is a square grid designed to make it easy to create square graphs for insertion into word processing documents. The full power of Geogebra is behind it. To copy the graph you've made, choose "Graphics View to Clipboard" from the Edit menu.

Practice writing linear equations

This applet that I developed using Geogebra generates a line, asks the user to provide an equation and then indicates whether the submitted equation is correct.