Education Technology

Parametric, Vector, Polar and 3-D functions

Published on 06/09/2008

Activity Overview

In this activity, students investigate and graph parametric functions, vectors, polar functions, and 3D functions.

Before the Activity

  • See the attached PDF file for detailed instructions for this activity
  • Print pages 69 - 78 from the attached PDF file for your class
  • During the Activity

    Distribute the pages to the class.

    Follow the Activity procedures:
    Parametric Functions:

  • Enter the two equations and graph them


  • Slope of a Parametric Curve, Chain Rule for Parametric Equations:
  • Find the derivative of the graph and approximate the slope


  • Arc Length of Parametric Curves:
  • Enter the parametric functions, graph the arc, and find the arc length


  • Parametric Equations for Trajectories:
  • Enter the differential equations and solve them
  • Graph the parametric equations and find the solution


  • Symbolic and Graphical Representation of Vectors:
  • Enter the parametric equation and define the position vector function
  • Define the first and second derivative of the position vector and graph each vector


  • Area Bounded by Polar Curves:
  • Enter the equations and graph the polar functions
  • Enter the definite integral and find the area


  • 3D Functions:
  • Enter the equation and graph to see the surface
  • After the Activity

    Students will complete the practice exercise problems.

    Review student results:

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