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Thread: How do change the default period in a sine or cosine wave to π or 3π instead of 2π

  1. #1

    How do change the default period in a sine or cosine wave to π or 3π instead of 2π

    OK, so in the trigonometry graph I am able to plot phase shift and vertical shifts of sine and cosine waves.Click image for larger version

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    However, I am not able to get it to do a different period, such as π. The default period is of course 2π. But how can I get it to do 1/2 or 3π or something crazy like that?

    Thanks.

    Rob

  2. #2
    Sketchpad Developer
    Join Date
    Oct 2010
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    Philadelphia
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    Hi Rob,

    You would find it interesting and hopefully enlightening to experiment with a variety of ways to transform the sine function. Consider starting with a function expressed as y = a sin (bx + c) + d. Use initial parameter values of a=1, b=1, c=0, and d=0 so that your initial expression is equivalent to y = sin (x). Then experiment with changing each of the parameters in turn to see its effect -- but first, before changing a parameter, think carefully about the effect it will have and make a prediction about how the graph will change. The objective, of course, is to develop a clear understanding and explanation of the transformation that results from changing each parameter, and as a result to be able to create (for instance) a sine wave with an amplitude of 0.5, centered on the line y = -2, and with maximum values at x=0 and at x=pi/2. (In other words, given an amplitude, vertical offset, period, and phase shift, you should be able to immediately change the parameters to produce the desired graph.)

    --Scott

  3. #3
    Stek,

    I go to Number - Calculate and I try to put in y=sin(bx+c)+d and it doesn't let me. Do you use Number - Calculate to make this equation? I am able to manipulate amplitude, but not phase shift, verticle shift or period. So I need more detailed instructions on how to make Sketchpad do this operation.

    OK, I have managed to get phase shift and verticle shift by doing sin(x+π) but I still can't change the period. If I do something like sin(3π) I just get a straight line, or sin(π/2) still a straight line.
    Last edited by Robwinfield; 07-01-2012 at 06:46 PM.

  4. #4
    Hi Rob,

    You'll need to create parameters for the coefficients and constants (b, c, d, n). Choose Number|New Parameter.

    A couple of resources may be helpful. The first is this Algebra tutorial––it isn't about Sine curves, but it will get you started using parameters with functions: http://learningcenter.dynamicgeometry.com/x24.xml

    Also, on the first and third Tuesday of each month, we offer free Sketchpad webinars. These are a nice way to get a focused Sketchpad "lesson" from an experienced Sketchpad user. You can see the schedule here: www.keycurriculum.com/webinars.

    Finally, we do have six-week moderated online courses that will guide you in digging more deeply into Sketchpad. These aren't free, but they are very reasonably priced.

    Happy sketching!

    Elizabeth

  5. #5
    Thanks for the nice information in this post dear...
    clark

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