Polar Equations

By: Diana Brown

(1) Investigate

When a
and b are equal (in this case a and b both equal one), and k is an integer,
this is one textbook version of the “ n-leaf rose.”

K = 1 K = 2

K = 3 K = 4

K = 5 K = 6

K = 7 K = 8

K = 9 K = 10

Notice that k determines the number of “leaves/pedals” on
the “rose.”

Click here to open a Graphing
Calculator file to animate the graph as k varies.

(2) Investigate and compare

for various k.

K = 3 K
= 4

K = 5 K
= 6

Notice that if k is odd then the number of pedals is equal
to k, but if k is even then the number of pedals is 2k.

(3) Investigate the same equation as # 2, but replace
cosine with sine.

K = 3 K
= 4

K = 5 K
= 6