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:
