Education Technology

Exploring functions with CAS

Published on 06/09/2008

Activity Overview

In this activity students use the CAS tool to explore sin, cos, and tan functions. They expand the functions and find the domain. They also prove the conjectures.

Before the Activity

  • See the attached PDF file for detailed instructions for this activity
  • Print pages 1 - 4 from the attached PDF file for the class
  • During the Activity

    Distribute the pages to the class.

    Follow the Activity procedures:

  • Consider a cos function and expand it
  • Note the function is even if n is even and odd if n is odd
  • Consider a sin function and expand it
  • Note for all n the function is odd
  • Consider a tan function and expand it
  • If n is even , the denominator has degree n and the numerator has degree n - 1, and if n is odd, the numerator has degree n and the denominator has degree n - 1
  • Prove the above statements using CAS
  • Graph and find the zeros of the functions
  • After the Activity

    Review student results.

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