Let a=b and k=2
Notice that they all have 2 "leaves"
and that the intercepts are 0, 2a, and -2a. Now we will let k=1
and a and b will remain the same as above.
Now we see that there is one leaf.
We notice that the graph with a negative value for a=b is pointing
to the left.
Now examine the same three equations
All graphs have 6 leaves.
Now let us compare these with
The red graph has 4 leaves or 2k and
the blue graph has 2k=20 leaves.
Next we will look at k= 3 and 7.
We notice that when k = an odd number,
then the graph will have k number of leaves, and when k= an even
number the graph will have 2k number of leaves.
Now we will replace cosine with sine.
We notice a shift of 90 degrees.
These are FUN!!