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Math Help - three functions

  1. #1
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    three functions

    if sin(radian) is for x,
    and cos(radian) is for y,
    what is for z?


    this might noght be descriptive enough, so feel free to ask for clarification

    thank you
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  2. #2
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    I'm guessing you mean for the Cartesian co-ordinate system, what the trigonometric functions are.

    Sine is for the y-axis, and Cosine is for the x-axis. You have it the wrong way around.
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  3. #3
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    You can think of the x,y plane as the "top" of a cylinder. The important things on the top can be defined by (x,y) co-ordinates, or (r, \theta) coordinates, where x = r\cos{\theta} and y = r\sin{\theta}.

    The height of the cylinder is defined by the length on the z axis in 3D space. Since this doesn't depend on x or y, it doesn't depend on r or \theta either. Therefore, z is just z.

    So to answer your question

    x = r\cos{\theta}

    y = r\sin{\theta}

    z = z.

    These are known as Cylindrical Polar Co-ordinates.
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  4. #4
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    Or it could be the Spherical coordinate system, which if you draw a line 1 unit and move it about the origin, then find where the furthest point is from the origin.

    If this is the case, then x is no longer just cosine and y is no longer just sine, because as you move it about (0,0,0) through the z-axis as well, then it will be shorter than just sin(x) and cos(x).

    \displaystyle{x=r*sin(\theta)*cos(\phi)}

    \displaystyle{y=r*sin(\theta)*sin(\phi)}

    \displaystyle{z=r*cos(\theta)}
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