www.jjw3.com > http://precalc.jjw3.com/math1113.htm > http://precalc.jjw3.com/math1113/F10Math1113Proj1.htm

john{dot}weber{at}gpc{dot}edu

This project is due on 3 November 2010.  You must complete the project with a partner. Normally, all members of the group will receive the same grade; however, the instructor reserves the right to conduct individual interviews over the content of the project and to assign different grades to different members of the group.

Introduction

We have spent several class periods discussing trigonometric functions. Now, I want you to generalize your knowledge about amplitudes, periods and phase shifts of trigonometric functions.

Questions

1. 1. (2 points) Find a function f(x) = Asin(Bx + C) + D that models the monthly average minimum temperature (in °F) of Atlanta from 1993 to 2002^*.
   2. (1 point) Graph the data with your function on the same set of axes.
   3. Data:
      
      

      JAN	FEB	MAR	APR	MAY	JUN	JUL	AUG	SEP	OCT	NOV	DEC
      35.57	38.67	43.86	51.55	60.6	67.76	71.56	70.59	64.43	53.7	43.79	37.14

2. 1. (2 points) Find a function f(x) = Esin(Fx + G) + H that models the monthly average maximum temperature (in °F) of Atlanta from 1993 to 2002^*.
   2. (1 point) Graph the data with your function on the same set of axes.
   3. Data:
      
      

      JAN	FEB	MAR	APR	MAY	JUN	JUL	AUG	SEP	OCT	NOV	DEC
      53.85	58.03	64.54	72.97	80.83	86.19	90.36	88.66	82.53	72.91	63.14	54.51

^*Data obtained from NCDC. NCDC climate data online. (Retrieved 3 November 2003 from http://cdo.ncdc.noaa.gov/CDO/cdo).

3. 1. (1 point) Find a data set that is cyclical and find a function f(x) = Ksin(Lx + M) + N that models the data. You must cite the data using valid APA citation.
   2. (1 point). Graph the data with your function on the same set of axes.

Technology Assistance

You are encouraged to use software (e.g., Mathematica, Maple, other) or use the TI-83/84 to find the models for the data and to plot the data and the functions. For the x-values, use x = 0 for Jan; x = 1 for Feb; …; x = 11 for Dec.

To find the model using the TI83/84, complete the following steps:

1. Type x-values into list L₁: see http://stats.jjw3.com/math1431/ti83list.htm;
2. Type y-values (i.e., temperatures) into list L₂;
3. Set-up sine model: STAT key; right arrow key; scroll down to SinReg; ENTER;
4. Type list names where data is located: 2nd; press 1; comma; 2nd; press 2;
5. Execute: ENTER;

The resulting screen contains the model for the data in the form y=a*sin(bx+c)+d and the values for a, b, c, and d are given below the model.

To construct a plot of the data using the TI83/84, see http://stats.jjw3.com/math1431/ti83scatter.htm.

Final Report

You are to present a written report describing your findings. Include the following items:

• A conclusion (2 points) that summarizes your findings, including the graphs; and including other data as necessary.

Please follow these guidelines when preparing your report:

• Papers should include a mixture of tables, graphs, equations, and written explanations. Your textbook can serve as a model. For example, look at the equations, tables, and graphs in your textbook and notice the way the text inserts these into the flow of its written explanations. In particular, note that an equation is usually easier to read if centered on a line by itself.
• Papers should be typed. You may write equations and formulas in by hand or you can use the built-in equation editor in Microsoft Word. Click on Insert on the command bar, select Object, and select Microsoft Equation. If you use Microsoft Word at home, you may need to install this feature. Use the built-in help feature to look for instructions to "install or remove individual components".
• Clearly explain your reasoning. Focus on explaining what you are doing conceptually, not on the mechanics of the algebra. You may assume that the intended reader has a working understanding of the mathematics.
• You are not writing a user's manual on how to use the calculator. Do not write about which keys you pressed on your calculator.
• Turn in one paper per group. The instructor will keep all papers. Make a copy for your files before turning in your paper.
• You will be graded on the quality and clarity of your written presentation as well as the mathematical accuracy of your paper.