Investigate
When a, b and k equals 1, the graph looks like this:
Let's keep a and b equal to one and vary k. When k = 2 the graph looks like this:
We get two leaves. Let's try k = 3, 4 and then 5.
It seems as k increases the number of leaves increases. In fact, the number of leaves equals k.
Compare with
When b and k equals 1, the graph looks like this:
Now the graph looks like a circle. Let's see what happens when we change k to 2.
Four leaves! Let's look at the graph when k = 3, 4, and 5, respectively.
It looks as if the number of leaves equals k when is is odd, but doubles k when it is even.
What if . . . cos ( ) is replaced with sin( )?
When a, b and k equals 1, the graph looks like this:
It rotated! Let's keep a and b equal to one and vary k. When k = 2 the graph looks like this:
Same graph as cos, but rotated again! Let's try k = 3, 4 and then 5.
Again, all the same graphs as cos, but rotated. Let's compare with b sin (k0).
When b and k equals 1, the graph looks like this:
Let's see what happens when we change k to 2.
Let's look at the graph when k = 3, 4, and 5, respectively.
Just as I suspected, the same graphs as above, but, rotated!
