Assignment #10:

Altering Parametric Equations

 

By Amber Krug

 


 

       Consider the graph of the parametric equation

                            

                                    x = cos (t)

                                    y = sin (t)

 

                                    for 0 t 2p

 

which is:

 

 

 

We can manipulate the equation so that the graph is altered.

 

We can insert a variable before the functions:

 

                                    x = a cos (t)

                                    y = b sin (t)

 

                                    for 0 t 2p.

 

       When a = 2 and b = 1, our graph takes on an elliptical shape:

 

 

       We can also alter the equation so that there is a variable in front of t:

 

x = cos (at)

                                    y = sin (bt)

 

                                    for 0 t 2p.

 

       When a = 2 and b = 4, our graph takes on the shape of a bowtie:

 

 

 


 

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