# Thread: What is 't' in parametric equations?

1. ## 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.

2. Because t is a real number it is taken to be radian measure.
2 pi corresponds to 360 degrees. So just do the conversions.

3. 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.