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

    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:

      JANFEBMARAPRMAYJUNJULAUGSEPOCTNOVDEC
      35.5738.6743.8651.5560.667.7671.5670.5964.4353.743.7937.14
    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:

      JANFEBMARAPRMAYJUNJULAUGSEPOCTNOVDEC
      53.8558.0364.5472.9780.8386.1990.3688.6682.5372.9163.1454.51

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

    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:

Please follow these guidelines when preparing your report: