ࡱ> 1BDAJKLMNOPQRSTUVi j k l m n o p q r s t u v w x y z { | Q` 1lbjbjss 4pC[ EEE8E\PFf0GHL0I0I0IRRRҵԵԵԵԵԵԵ$hQvERRRRR 0I0I =gWgWgWR B 0I0IҵgWRҵgWgWJ\0I$G Pj 0 ESSBS00ǺTǺǺ. RRgWRRRRR#UDRRRRRRR$ : :  Graphs of Sine, Cosine Functions Describing sinusoidal curves with Amplitude, Period, Phase Shift SEQ PartNum \* Arabic 1) Find the amplitude, period, and phase shift of each equation, then graph it, showing at least one period (cycle).  EMBED Equation.3  (Remember that phase shift is the same as C, and that you might have to do some math to put the above equation into the familiar  EMBED Equation.3  format) Amplitude: Period: Phase Shift:  EMBED PBrush   Describing sinusoidal curves with Amplitude, Period, Phase Shift SEQ PartNum \* Arabic 2) Write out an equation of a sine function, given the following characteristics, then graph it. Amplitude: 3 Period: 2 Phase Shift:  EMBED Equation.3   EMBED PBrush   SEQ PartNum \* Arabic 3) Write out an equation of a sine function, given the following characteristics, then graph it. Amplitude:  EMBED Equation.3  Period:  Phase Shift:  EMBED Equation.3   EMBED PBrush  Modeling Using Sinusoidal Regressions Goal: Given some data, find a sinusoidal function (if one exists) for it, with the help of your calculator.For each of the following exercises, you should follow these steps: Turn your calculators diagnostics on Press  INCLUDEPICTURE "http://www.prenhall.com/divisions/esm/app/calc_v2/calculator/medialib/Technology/Documents/TI-83/Images/TI-Gifs/2nd.gif" \* MERGEFORMATINET  INCLUDEPICTURE "http://www.prenhall.com/divisions/esm/app/calc_v2/calculator/medialib/Technology/Documents/TI-83/Images/TI-Gifs/0.gif" \* MERGEFORMATINET  for the Catalog option, then press  INCLUDEPICTURE "http://www.prenhall.com/divisions/esm/app/calc_v2/calculator/medialib/Technology/Documents/TI-83/Images/TI-82-Gifs/Exp-1.gif" \* MERGEFORMATINET  (for the yellow D, above it). Push the down arrow  INCLUDEPICTURE "http://www.prenhall.com/divisions/esm/app/calc_v2/calculator/medialib/Technology/Documents/TI-83/Images/TI-Gifs/DCur.gif" \* MERGEFORMATINET  until you get to DiagnosticOn, then press  INCLUDEPICTURE "http://www.prenhall.com/divisions/esm/app/calc_v2/calculator/medialib/Technology/Documents/TI-83/Images/TI-Gifs/Ent.gif" \* MERGEFORMATINET . That gets you back to the home screen. Press  INCLUDEPICTURE "http://www.prenhall.com/divisions/esm/app/calc_v2/calculator/medialib/Technology/Documents/TI-83/Images/TI-Gifs/Ent.gif" \* MERGEFORMATINET  again to actually turn the diagnostics on. You only need to do this ONCE, but its not bad to get the practice of doing this. Input the data into your calculator On the TI-83, use the  INCLUDEPICTURE "http://www.prenhall.com/divisions/esm/app/calc_v2/calculator/medialib/Technology/Documents/TI-83/Images/TI-Gifs/Sta.gif" \* MERGEFORMATINET  key, then select Edit, which is what you start at. Add the data to lists L1 and L2. You should add your "X" data to the L1 list, and your "Y" data to the L2 list. When you're done, you should be able to read down the columns, and see (X,Y) on the same row, with X under the L1 list, and Y under the L2 list. Graph the points (scatter plot) On the TI-83, use the  INCLUDEPICTURE "http://www.prenhall.com/divisions/esm/app/calc_v2/calculator/medialib/Technology/Documents/TI-83/Images/TI-Gifs/2nd.gif" \* MERGEFORMATINET  INCLUDEPICTURE "http://www.prenhall.com/divisions/esm/app/calc_v2/calculator/medialib/Technology/Documents/TI-83/Images/TI-Gifs/y_.gif" \* MERGEFORMATINET  keys, select Plot1, which is what you start at. Select On, then press  INCLUDEPICTURE "http://www.prenhall.com/divisions/esm/app/calc_v2/calculator/medialib/Technology/Documents/TI-83/Images/TI-Gifs/Gra.gif" \* MERGEFORMATINET . Fit the Sine Curve To the Data Using what you know about fitting sine curves to points, figure out what the equation must be. As you're working, put your 'rough drafts' of the equation into the calculator, so you can see if it looks right, before you do the work of typing in the whole thing. Remember that if you want to INSert something into your equation, rather than overwriting what's there, you should push the  INCLUDEPICTURE "http://www.prenhall.com/divisions/esm/app/calc_v2/calculator/medialib/Technology/Documents/TI-83/Images/TI-Gifs/2nd.gif" \* MERGEFORMATINET  INCLUDEPICTURE "http://www.prenhall.com/divisions/esm/app/calc_v2/calculator/medialib/Technology/Documents/TI-83/Images/TI-Gifs/Del.gif" \* MERGEFORMATINET  key in order to access the INS functionality (in yellow).  SEQ PartNum \* Arabic 3) Enter the following data, and draw a scatter plot from it, and then finally figure out the equation, in terms of amplitude, vertical shift, period, and phase shift. Month X value we'll use to represent the month Average Temperature, in F Jan 29.7 Feb 33.4 Mar 39.0 Apr 48.2 May 57.2 Jun 66.9 Jul 73.5 Aug 71.4 Sep 62.3 Oct 51.4 Nov 39.0 Dev 31.0 First plot the above data points on your calculator. This will allow you to visually confirm that the data is, indeed, periodic, and looks like a sine wave. Next, calculate the vertical stretch (the amplitude), vertical shift, horizontal stretch, and horizontal offset, using what you know. As you calculate each, try graphing your sin function with that new number, so as to confirm that it looks right (i.e., double-check your work as you go). 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