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