# Activities

• • • ##### Subject Area

• Math: Calculus: Applications of the Derivative

• ##### Author 9-12

60 Minutes

• ##### Device
• TI-89 / TI-89 Titanium
• ##### Other Materials
This is Activity 8 from the EXPLORATIONS Book:
Advanced Placement Calculus with the TI-89.

## 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.

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