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: