Explorations with Geogebra

1. Explorations with Geogebra Jeff Morgan jmorgan@math.uh.edu Talk Slides: www.math.uh.edu/~jmorgan/hollyer

2. Disclaimer… The following examples are not necessarily exciting. They were chosen to illustrate some interesting features of Geogebra.

3. Example 1 Use Geogebra create the graphs of the cosine and sine functions from the unit circle, without specifically using calls to sin(x) and cos(x).

4. Example 2 Use Geogebra to graph the function f (x) = sin(x). Then create a tangent line to the graph at some value of x. Compare the tangent line to the graph. Finally, animate the change in the tangent line as the value of x is changed.

5. Example 3 Use Geogebra to animate the drawing of the parametric curve (cos(3t),sin(2t)).

6. Example 4 A 10 foot fence sits 2 feet from a 50 foot tall building. What is the length of the shortest ladder than can have its base on the opposite side of the fence from the building, with its top touching the building? Solve the problem without doing any calculations!

7. Example 5 A rectangle is has its base on the x-axis and its upper vertices on the graph of y = cos(x) for x between -p/2and p/2. Create the graph of the curve who x-coordinate is the lower right hand vertex and whose y-coordinate is the area of the rectangle. This curve looks a little like a parabola? Determine whether it is a parabola. Solve the problem without doing any calculations!

8. Example 6 Graph the function f (x) = 4 - (x³ + 1)1/2. Then pick a value x = a between 0 and 5, and find the integral of f (x) from 0 to a. Show graphically what this integral represents. Then vary the value of a and graph the output as a function of a.