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