EMAT 6680 Assignment 10:

Parametric Curves

By

Victor L. Brunaud-Vega

 Graph If we give a range of values to t from 0 to 2¹, then we have a longer movement of the curve generating a circle with center in (0,0) and a radius of 1.   Given that my only variable is t, I would try to give it different values and see what happens. In order to explore other possibilities using this formula, I will add two new parameters: x=cos (at) y=sin (bt)   If I give different values to only one of the variables (a or b), keeping the other with a value of one and t on the range of 0 to 2¹.  To have an idea of the effect in the graph because of the variances on the formula, these values should include at least two even numbers, two odd numbers, a couple of fractional numbers and all of them once in positive and once in negative form.  This should be enough.   Follow the sequence below, keeping a=1 and 0 < t > 2¹, I selected graphs with different values for b: If it is still not clear, you can watch the movement of the curve in this movie. Now, let us keep b=1 and 0 < t > 2¹, and graph different values for a: It looks like the same kind of movement but this time the line of symmetry is vertical (y axis).  You can watch the entire movement of the curve in this movie.