When Charlie explains how he is looking for counterfeit money, he mentions that the engraving on the borders of paper money uses a technique called guilloche. The overall design is very intricate but is produced using a combination of graphs of variations of the sine curve, called sinusoids.
This activity uses elementary sine graphs to demonstrate how changes in the phase shift, amplitude, and period of the sine function affect its graph.
Before the Activity
Download the attached PDF and look over the Teacher Page.
During the Activity
Discuss the materials from the Student Page with your class.
After the Activity
Encourage students to explore web sites and questions from the Extensions Page.