The Sine Curve






Exploring the Sine Curve using the Casio 9850 Dynamic 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 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

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.