**Assignment 11:**** Polar Equations**

**Ebru Ersari**

**Investigate r = a + b cos(k)**

First, I assumed, a = b = k = 1.

I wondered what if we change only one variable each time. a = b = 1, k = 2; a = k = 1, b = 2; b = k = 1, a = 2.

I played with the equation by changing the variables.

Then, I drew the graphs of r=b cos(k) for different b and k values (a=0).

Here is the animations of r = a + b cos(k) for different k values (a = 1, b = 1, -10 < k < 10) and r = b cos (k) for different k values (b = 1, -10 < k < 10)

I used the same steps for the equation r = a + b sin (k). First, I assumed, a = b = k = 1.

I drew the graphs of r = a + b sin (k) for a = b = 1, k = 2; a = k = 1, b = 2; b = k = 1, a = 2.

I drew some graphs of the sine equation for different values.

Next, I drew the graphs of the sine function r = b sin (k) for different b and k values (a = 0).

Here is the animations of r = a + b sin (k) for different k values (a = 1, b = 1, -10 < k < 10) and r = b sin (k) for different k values ( b = 1, -10 < k < 10)