Education Technology

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.

    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
  • 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