# Activities

• • • ##### Subject Area

• Math: Precalculus: Parametric Equations
• Math: Precalculus: Polar Equations

• ##### Author College

60 Minutes

• TI-86
• ##### Other Materials
This is Activity 3 from the EXPLORATIONS Book: Using the TI-86 in Collegiate Mathematics: A Tutorial

## Parametric and Polar Graphing

#### Activity Overview

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

#### 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
• #### During the Activity

Distribute the pages to the class.

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
• #### 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