1. Investigate the equation

for various values of 'k', where a = b and k is an integer.

2. Then compare with

for different values of 'k'.

3. Also, explore replacing .....cos() with sin()?

Investigation of the graphs of the following equation when a = 1 = b and k is an integer from 1,,7.

**For k = 1,**

**For k = 2,**

**For k = 3,**

**For k = 4,**

**For k = 5,**

**For k = 6,**

**For k = 7,**

**Comparison
of ** and for three different
values of k.

**For k = 2,**

**For k = 3,**

**For k = 4,**

*Notice that
when k is an even integer (2 or 4 in this example), the number
of leaves on the rose doubles when the a variable is omitted from
our polar equation. On the other hand when k is odd (3 in this
case), the number of leaves on the rose are equal.*

**Substituting
sin() for cos() in the equation **

**will change
our graphs as follows (for k = 3, 4, 5, & 6):**

**Substituting
sin() for cos() in the equation **

**will change
our graphs as follows (for k = 2, 3, 4, & 5):**