Education Technology

Parametric, Vector, Polar and 3-D functions

Subject Area
Math: Calculus: Applications of the Derivative
Math: AP Calculus: AP Calculus
Level
9-12
Activity Time
60 Minutes
TI Calculator
TI-89 / TI-89 Titanium
Other Materials
This is Activity 8 from the EXPLORATIONS Book:
Advanced Placement Calculus with the TI-89.
Resource Types
Lessons

Parametric, Vector, Polar and 3-D functions

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
  • Subject Area
    Math: Calculus: Applications of the Derivative
    Math: AP Calculus: AP Calculus
    Level
    9-12
    Activity Time
    60 Minutes
    TI Calculator
    TI-89 / TI-89 Titanium
    Other Materials
    This is Activity 8 from the EXPLORATIONS Book:
    Advanced Placement Calculus with the TI-89.
    Resource Types
    Lessons
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