WebQuest

Finding the Equation of a Sine Curve Using Biorhythm Graphs

Process

20100605100524aReZy.bmp

Part 1:  Obtaining sine equations from the period, amplitude, phase shift and vertical shift of a graph.

1.  Create your personalized biorhy
thm graphs by going to the following website: Biorhythms.

Enter your birth date and enter June 22 for the biorhythm date. Pick XLarge for the size and 44 for the width.  When you click on go, your personalized biorhythm graph will be generated and you will see three sine graphs.  Print your personalized biorhythm graph.

2.  Write the equations of the three sine graphs (
Physical, Emotional and Intellectual) in the form y = d + asin[b(x-c)].

Go to the following websites to review the concepts of period change (b) ,amplitude change (a), phase shift (c), and 
vertical shift (d).

The following website has an applet that demonstrates the transformations of the sine wave ans the parameters are changed:  sine wave applet.

 
Part2:  Obtaining sine equations using sine regression with the graphing calculator.

1.  Make a grid on your biorhythm graph.  Your horizontal axis (x) will be the line on the far left (5/31) and your vertical axis (y) will be the horizontal line down the middle (0).

Draw
vertical lines through the following days: 6/2, 6/5, 6/8, 6/11, 6/14, 6/17, 6/20, 6/23, 6/26, 6/29.
Divide the vertical axis in a scale of ten (where 0 is in the middle). 
  
2.  Fill out the tables in the attachment below with the information obtained from the biorhythm graphs using the grid you made.

3.  Follow the instruction for the sine regression with the TI calculator (attachment below) to obtain regression equations from the data collected on the tables from your personalized biorhythm graphs
(Physical, Emotional and Intellectual).


Part 3:  Biorhythm predictions for the day of the final exam and Percent Error.

1.  Use the
Physical, Emotional and Intellectual estimated equations obtained in Part 1 to predict what will be your biorhythms on June 22.  In other words, find the value of your equation when x = 22.  

2. 
Use the Physical, Emotional and Intellectual equations obtained in Part 2 to predict what will be your biorhythms on June 22.  In other words, find the value of your equation when x = 22. 

3.  Use the predictions obtained to calculate the percent error for each biorhythm
(Physical, Emotional and Intellectual) using the estimated equations results.

4. 
Use the predictions obtained to calculate the percent error for each biorhythm (Physical, Emotional and Intellectual) using the regression equations results.      

Attachments


File
  • File
    Description: Instructions for Sine Regression with TI Calculator

File
  • File
    Description: Tables for Biorhythm Graphs

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