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Activity Overview

In this activity, students explore parametric and polar graphing on the TI-86.

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Before the Activity

Set up the calculator as explained in the activity
See the attached PDF file for detailed instructions for this activity
Print pages 39 - 50 from the attached PDF file for the class
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During the Activity

Distribute the pages to the class.

Follow the Activity procedures:

Graphing a Circle using Parametric Equations:

Enter a pair of parametric equations
Plot the graph obtained by connecting the points obtained with the t-values
Change the setting of tStep and regraph
Use ZSQR option and view the graph; note the values of tMin, tMax, or tStep
Use negative tStep values to graph the parametric equations
Graphing the Inverse of a Function:

Graph a one-to-one function in parametric mode
Graph the inverse of the function
Set the viewing window and graph the function and its inverse together
Observe the symmetry of the function and its inverse with respect to the y = x line
Finding Roots of 1:

Recall that the *n* nth roots of 1 are given by x + iy, where (x, y) are the n points on a unit circle
Use the parametric mode and the Trace feature to find the roots of 1
Graphing a Cycloid:

Enter the parametric cycloid equations in the graph editor and observe the resulting graph
Get a better perspective of the shape of the graph with the help of the ZSQR feature
Modify the parametric equations to obtain an inverted cycloid
Graphing a Line Segment:

Enter a pair of parametric functions, set the window, and observe the graph of a line segment joining two points in the plane
Polar Graphing:

Enter the polar equation of the four-leaved rose and graph the function
Find the rectangular coordinates of a point on the curve, given the value of θ
Change the graph format mode to display polar coordinates
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After the Activity

Students complete the exercises on the Activity sheet.

Review student results:

As a class, discuss questions that appeared to be more challenging
Re-teach concepts as necessary