The Cosine Curve

Materials

Casio CFX 9850G+ Graphing Calculator

Exploring the Cosine Curve using the Casio 9850 Dynamic Graphing Function

This lesson is intended to follow a lesson on periodicity and symmetry of graphing functions.The students should be experienced with graphing functions for the lesson to go smoothly. The lesson enables the student to discover the relationship of constants on the cosine function. The lesson can also be done using the dynamic graphing function. See the Sine Curve Lesson for an example with dynamic graphing.   

It is assumed that the students have graphed y = cos(x)
Choose the graph mode from the main menu Set the view window or range to:

Xmin = -2(pi)
Xmax = 2(pi)
scale = (pi)/4
Ymin = -6
max = 6
scale = 1

Enter 3 equations of the form

y = Acos(x)
Y1 = 2cos(x)
Y2 = 4cos(x),

change equation to orange Y3 = 6cos(x),
change equation to green
Graph all three equations (F6)

Student Questions

Describe what happens to the graphs as A changes?
What happens to the period?
What happens to the amplitude?
Enter 3 equations of the form

y = cos(Bx)
y = cos(2x)
y = cos(4x),

change equation to orange y = cos(6x),
change equation to green
Graph all three equations (F6)

Student Questions

Describe what happens to the graphs as B changes?
What happens to the period? What happens to the amplitude?
Enter 3 equations of the form

y = cos(x + C)
y = cos(x + 2)
y = cos(x + 4),

change equation to orange y = cos(x + 6),
change equation to green
Graph all three equations (F6)

Student Questions

Describe what happens to the graphs as C changes?
What happens to the period?
What happens to the amplitude?
Enter 3 equations of the form

y = cosx + D
y = cosx + 2
y = cosx + 4,

change equation to orange y = cosx + 6,
change equation to green
Graph all three equations (F6)

Student Questions

Describe what happens to the graphs as D changes?
What happens to the period?
What happens to the amplitude?
Predict what will happen for each of the following,
then graph to check you assumption:

y = cos5x
y = 6 cos2x
y = 3 cosx
y = 2 cos3x
y = 2 cos(x + 3)
y = cos3(x + 2)
y = 4cos2x
y = 3cos2(x + 4)

Submitted by Submitted by: Chris Camacho, University of Central Florida, undergraduate mathematics education major. University of Central Florida