www.jjw3.com > http://precalc.jjw3.com/math1113.htm > http://precalc.jjw3.com/math1113/F10Math1113Proj1.htm
john{dot}weber{at}gpc{dot}edu
Fall 2010 Precalculus Project 1
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

 (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^{*}.
 (1 point) Graph the data with your function on the same set of axes.
 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 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^{*}.
 (1 point) Graph the data with your function on the same set of axes.
 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).

 (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.
 (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 TI83/84 to find the models for the data and to plot
the data and the functions. For the xvalues, 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:
 Type xvalues into list L_{1}: see http://stats.jjw3.com/math1431/ti83list.htm;
 Type yvalues (i.e., temperatures) into list L_{2};
 Setup sine model: STAT key; right arrow key; scroll down to SinReg; ENTER;
 Type list names where data is located: 2nd; press 1; comma; 2nd; press 2;
 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 builtin 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
builtin 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.