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lvl10720-Turquoise
20-Turquoise
March 16, 2017
Solved

Plotting the points of intersection on the graph ?

  Hello Everyone.

  From :

(1).PNG

  To the question : Plotting the points of intersection on the graph ?

         Thanks in advance for your time and help.   

Fred_KohlheppAnswer
23-Emerald I
March 17, 2017

Emperically:

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8 replies

LucMeekes23-Emerald V
23-Emerald V
March 16, 2017

The points where the curve intersects with itself are plotted on the graph.... along with a lot of other points.

If you want the coordinates of the intersection points plotted in readable text next to them, you need to define a few more curves to get them in.

Refer to the great work "Creating amazing images with mathcad" by Byrge Birkeland for ideas on how to do that.

Success!
Luc

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Werner_E
Werner_E25-Diamond I
25-Diamond I
March 16, 2017

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    lvl10720-TurquoiseAuthor
    20-Turquoise
    March 17, 2017

    (2).PNG

       How many points of intersection on the graph ?

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    LucMeekes23-Emerald V
    23-Emerald V
    March 17, 2017

    Sorry, I misunderstood your original question.

    To solve the problem at hand, I would mathematically create the lissajous-shape in 3D, then make a projection of it on a (2D) surface and find the intersecting points of it.

    Why the detour? because now you only have two expressions, and a single running variable. I see no path where that brings you to more than 2 solutions.

    Success!
    Luc

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    lvl10720-TurquoiseAuthor
    20-Turquoise
    March 18, 2017

        I greatly appreciate all of your time and help. Werner, Luc, and Fred.       . I'm very, very happy. And I think I still need help with the two of question, the above, on cos(  ) function :

    (3).PNG

                  Thanks in advance.
                        Best Regards.

                               Loi

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    lvl10720-TurquoiseAuthor
    20-Turquoise
    March 18, 2017

      From :

    (4).PNG

      So I have a query : How to rotate a graph (pi/2) clockwise and (pi/2) counter-clockwise ?

            Best Regards.

                  Loi 

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    Werner_E
    Werner_E25-Diamond I
    25-Diamond I
    March 18, 2017

    > How to rotate a graph (pi/2) clockwise and (pi/2) counter-clockwise ?

    clockwise: replace the x(t) on the abscissa by y(t) and the y(t) on the ordinate by -x(t)

    counter clockwise: replace the x(t) on the abscissa by -y(t) and the y(t) on the ordinate by x(t)

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