Students will use an online graphing tool called Desmos to investigate the horizontal shifting of the graphs of trigonometric functions as the value of C is changed in the functions:

y = sin(x-C) and y = cos(x-C)

This will be an active learning exercise where students will discover patterns for themselves. They will have some practice problems as well. Students who discover relationships for themselves have better problem solving skills and they retain the subject matter because it is not a memorization exercise. This activity can be done in a collaborative environment as well.

Prerequisite
1. Students have learned the basics of trigonometric functions
2. Students have learned functional notation
4. Students know how to graph a function by hand given a table of values
5. Students understand the domain and range of a function.
6. Students understand the meaning of amplitude, period and centerline of sinusoidal functions.

The Activity

Students are first given a simple sine or cosine function which have the a dynamic variable (C) subtracted from x. The graphs are either y = sin(x-C) or y=cos(x-C) They are asked to graph the function using a free online graphing program called Desmos with the value of C being a slider. They are then asked to move the slider and decide how the value of C shifts the graph horizontally.

The slider feature of Desmos allows a student to dynamically change the graph of a function as they change the equation by using the slider. This helps students to discover patterns in a much shorter space of time then it would take if the students graphed each graph by hand.

Students are asked follow-up questions to test their understanding of what they have learned.

What the Student will Discover

Students’ will discover how to shift the graph of a sinusoidal function horizontally by changing the value of C.