Investigate

When a and b are equal, the graph is like the following(a=b=2)
according to k=1, k=2, k=3, k=4.

To explore Click here
When a=b=2, the graph pass through
(4,0) and (0,0) regardless of the
value of k.

If **k** is
odd then the graph meets at 2 and
-2 with y-axis and if k is even
then it does at 4 and -4 with x-axis.

The number of leaves is the value of
k.

**What if the values of a and
b are different?**
**Case of a>b**.
Let's see the case of a=2 and b=1(k=1, 2, 3,4).
**Case of a<b**.
Let's see the case of a=1 and b=2(k=1, 2, 3,4).

**First observation**
If **a is bigger than b** then the figure becomes
to a **circle as the difference is bigger** regardless of k.
To explore Click here
If **b is bigger than a** then **new leaves**
appear and the size of new ones is difference of a and b. To explore
Click here

If then the graph is like the following(b=2)
according to k=1, k=2, k=3, k=4.

When b=2, the graph pass through
(2,0) and (0,0) regardless of the
value of k.

If k is even then it does at 2 and -2 with y-axis and x-axis.

If **k** is odd
then the number of leaves is the value of
k and if k is even then it is twice value of k.

**What if cosine function is
changed to sine function?**
In fact, we can expect a rotation
since sine function with addition of 90 degree becomes cosine
function.
The followings are graphs ofwhen a=2, b=2, and k=1, 2, 3, 4.

**Second observation**
The graph of is some degree rotation
of .
The rotation degree is decreasing as k is increasing.

Return to
Hyungsook's homepage