Assignment 10 :: Parametric Equations


By Jamie K. York



Let's explore the parametric equations below for 0 t 2.


x = a cos(t)

y = b sin(t)


As we saw with the quadratic equations, modifications of the variables resulting in various patterns in the resulting graphs. We will start with a value of 1 for both a and b. See the resulting graph below.




Note that this configuration results in a circle. To explore additional configurations where a = b, review the animated graph below.




What happens when these variables are not equal? Let's investigate further to see.




For each graph, one variable has been set constant at a value of 1. As the additional variable changes between 2 and 4, we notice that these modifications form the shape called an ellipse. This differs from the circle resulting from a = b. However, with either confirguration, it is clear that the values of a and b stretch or shrink the figure.


Note that for a t range of 0 t 2, the values of +a and -a result in the same graph. The same applies to the b variable.









Does the result change with a modification to the range of t? Explore the same graphs below with various t values to find out.


  0 t

  t 2






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