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Math Help - Contour Map

  1. #1
    Junior Member
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    Feb 2008
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    Contour Map

    I am fairly familiar with contour maps in the form f(x,y).

    But there is this problem:
    f(r,theta) = 1+sin(theta)-r with z = 1,3/4,1/2,1/4,0.

    I was thinking about transforming that into rectangular coordinates and somehow solve it that way, but even so, I do not know how to convert that.

    i TRIED to convert it and got y = root [(z-sin(theta)-1)^2-x^2]. If that is correct. how would I even map that?

    Pleaseee help
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  2. #2
    Member Mentia's Avatar
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    Bellingham, WA
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    Do you have any polar graph paper? That would make it easy to graph. Just set f(r,theta) equal to each of your z's and then solve for r in terms of theta. So for instance:

    z = 1 = 1+ sin(T) - r ----> r = sin(T)

    So start at theta=0 on your polar graph paper and then work your way counterclockwise calculating r along the way. Then do this for each z.

    Alternatively, if you must have cartesian coordinates, remember:

    r = (x^2+y^2)^(1/2)
    sin(T) = y/r = y*(x^2+y^2)^(-1/2)

    then f(r,theta) -> f(x,y) = 1 + y*(x^2+y^2)^(-1/2) - (x^2+y^2)^(1/2) = 1-\frac{x^2+(y-1) y}{\sqrt{x^2+y^2}}

    Good luck solving this for z... better stick with polar coordinates. Most calculators can be set into polar coordinates too.
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  3. #3
    Junior Member
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    Feb 2008
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    another question

    thank you, i drew the contour map and i guess it's correct.

    however, another question came up and it was, based on the contours in the previous problem, sketch the graph of the function f(r,theta) = 1+sin(theta)-r
    (same function) but for 0< f(r,theta) <1

    Isn't this the same thing as the previous problem? because from 0 to 1 is basically all the z values.
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