**Department of Mathematics Education**

**J. Wilson, EMAT 6680**

** **

Matthew Tanner

EMAT 6680

Write-up #11

July 16, 2004

Like the Cartesian
coordinate system, polar coordinates offer another unique description of the
location of a point in space. Whereas
points referred to using a Cartesian coordinate system refer to an original
point and reference
vectors. Sets of points described
simply using a Cartesian system are frequently cumbersome and protracted
using a polar system and vice versa.n-1 In this study, simple
polar equations of the form
are investigated.
Figure 1 Referring
to a Cartesian analogy of the graph of a polar equation, we see that within
the range of cycles because of the scalar multiple of 5. The
difference between the maxima and the mean of the graph (q for the cosine function without a scalar)
is 1. The mean amplitude of the graph (3
for the cosine function) is 0. 7
Figure 2 Polar graphs of equations of
the form is an even integer, the number of
“petals” is double – half correlating with the positive semi-cycles of the
Cartesian graph of the cosine function and half correlating with the negative
semi-cycles.k
Figure 3 When
and 0 coinciding with the graph of the function between p and p2.p |