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Math Help - What is 't' in parametric equations?

  1. #1
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    Question What is 't' in parametric equations?

    Please see the three pictures I enclose!

    I wonder what the 't' parameter really is in equations like this for an ellipse:

    x = xCenter + longaxis*cos(t)
    y = yCenter + shortaxis*sin(t)

    To my surprise, it is NOT the straight forward angle I thought it was!

    I want a triangle to "take a bite" out of an ellipse. I know the coordinates of its three corners, so I use the law of cosines to calculate the angle A which is at the center of the ellipse. That angle is the measure of the "bite".

    Then I draw the ellipse using parametric form. In my Matlab code I let the parameter angle go from 0 to 360-A. When A is 90 degrees or 180 degrees, it works as I want it too. But at for example 135 degrees, it doesn't. The ellipse is not drawn all the way, although I let the parameter t go from 0 to 225 degrees.

    So I must have misunderstood how that t-parameter works.

    Is there any way for me to transform a t-value to a real angle? For example, what must from 0 to t ust I use, in order for the ellipse to cover 235 degrees?

    EDIT:
    Of course, Matlab works in radians, I just translate it to degrees here to make it more intuitive.
    Attached Thumbnails Attached Thumbnails What is 't' in parametric equations?-135degrees.jpg   What is 't' in parametric equations?-90degrees.jpg   What is 't' in parametric equations?-180degrees.jpg  
    Last edited by Dirlewanger; March 15th 2008 at 03:41 PM. Reason: Corrected a typo
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  2. #2
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    Because t is a real number it is taken to be radian measure.
    2 pi corresponds to 360 degrees. So just do the conversions.
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  3. #3
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    Oh, yes I do work in radians. I just talk about the angles in degrees.
    Sorry for the confusion!

    The funny thing is that t works like an angle for increments of pi/2 (90 degrees), but not inbetween.
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