It appears that a affects the size of the rose. The length of the petals increases as the value of a increases. That is, if we were to construct a circumcircle about the rose whose center is (0,0), we can describe the length of a petal in terms of the circle's radius. In fact, the radius of the circumcircle is 2a. Negative values for a reflect the graph about the y-axis. Below are graphs of 5-petal roses with k = 5 (Review "What does k do?") and various values for a.
Observe these conclusions with the graphs below
then go on to "A
summary of r = 2a cos (kq)."
Below is a graph with k = 5 and a = 1.56. Click on the picture to observe how the size of the rose changes as a varies from -3 to 3.
