# The Cosine Curve

Exploring the Cosine Curve using the Casio 9850 Graphing Function

Materials: Casio CFX 9850G Graphing Calculator

####
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:* Chris Camacho, University of Central Florida,
undergraduate mathematics
education major. University of Central Florida