EMAT 6680 - Fall 2004

Assignment 11

Polar Equations

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By Keri Hurney

Using Graphing Calculator to investigate the 'n-leaf rose'

1. Investigate the equation

for various values of 'k', where a = b and k is an integer.

2. Then compare with

for different values of 'k'.

3. Also, explore replacing .....cos() with sin()?

Investigation of the graphs of the following equation when a = 1 = b and k is an integer from 1,,7.

For k = 1,

For k = 2,

For k = 3,

For k = 4,

For k = 5,

For k = 6,

For k = 7,

A colorful view of all of the 'roses' for k =1,,7:

Comparison of and for three different values of k.

For k = 2,

For k = 3,

For k = 4,

Notice that when k is an even integer (2 or 4 in this example), the number of leaves on the rose doubles when the a variable is omitted from our polar equation. On the other hand when k is odd (3 in this case), the number of leaves on the rose are equal.

Substituting sin() for cos() in the equation

will change our graphs as follows (for k = 3, 4, 5, & 6):

Substituting sin() for cos() in the equation

will change our graphs as follows (for k = 2, 3, 4, & 5):