# The Sine Curve

Exploring the Sine Curve using the Casio 9850 Dynamic Graphing
Function

Materials: Casio CFX 9850G Graphing Calculator

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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
make use of the dynamic graphing function which enables the student to
discover the relationship
of constants on the sine function. The lesson can also be done using
multiple graphs from the
graph function. See the Cosine Curve Lesson for an example without
dynamic graphing.

Choose the dynamic graph mode from the main menu

Enter function Y1: A(sin X)

Set the view window or range to:

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

Define the coefficients (F4)

Select A as the Dynamic Variable by highlighting A then (F1)
Set A = 1

Specify the dynamic variable range (F2)

Start: 1
End: 4
Pitch: 1

Choose dynamic graph speed stop and go (F3)

Press EXE

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Student Questions

Is this an even or an odd function?
What is the frequency?
What is the amplitude?

Press EXE several times.

What do you notice different about theses functions?
Did the period change?
Did the amplitude change?
For the general equation: y = a (sin x), what does a represent?

Exit to dynamic function screen

Change Y1 to Y1 = B + (sin X)

Select B as the dynamic variable by highlighting B then (F1)

Change dynamic graph range

Start: -2
End: 2
Pitch: 1
Change dynamic graph speed back to stop and go(F3)

Execute

What changed about the graph?
As you continue to press EXE:
Describe the Amplitude?
Describe the Frequency?
Describe the Period?
What can you conclude about the general equation: y = B + sin x ?
What would B represent?

Exit to dynamic function screen

Change Y1 to Y1 = sin CX

Select C as the dynamic variable

Change the dynamic graph range

Start: 0
End: 4
Pitch: 1
Choose dynamic graph speed as stop and go(F3)

As you continue to press EXE:

What changed about the graph?
Did the amplitude shift?
Describe the change of the period?
If the frequency changes, how does it effect the period?
What can you conclude about the general form y = sin cx?
What would C represent?
If C represents the frequency of the graph from 0 to 2(pi) , what is
the period?
What can you tell me about the graph of y = -1 + 2 (sin 3x)?
Have a student sketch y=-1+2(sin3x) on the board.
Have students graph the equation to check their assumptions.
What can we conclude about the graph of y = b + a(sin cx)?
*Submitted by:* Sandra Denis, University of Central Florida,
undergraduate
mathematics education major.