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Function riding on another function

  1. Jan 29, 2013 #1
    How do I write sin(x) where the x-axis is a function itself. For example, I want to write sin(x) along a half circle. I need to "wrap" the function, similar to "De Broglie wavelength" in image below.

    More specifically, I want to write f1 = 0.1*sin(x) the where the x-axis is f2 = sqrt(10^2 - x^2).

    I know that this generally will not pass the vertical line test. But for my application it will becuase the sin(x) has small amplitude compared to the circle radius.

    Attached Files:

  2. jcsd
  3. Jan 29, 2013 #2


    User Avatar
    Science Advisor

    Hey preposterous.

    One example like the diagram in your post would be in polar co-ordinates:

    r = 1 + 0.5*cos(theta)

    where in cartesian co-ordinates you use the relationship:

    r^2 = x^2 + y^2 and

    tan(theta) = y/x
  4. Jan 29, 2013 #3


    User Avatar
    Gold Member

    Why not

    0.1 * sin(sqrt(10^2 - x^2))
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