$\"\"$

\

The polar equation is $\"\"$ .

\

Graph the polar equation in cartesian plane: $\"\"$ on $\"\"$ .

\

$\"\"$

\

Observe the graph:

\

The equation $\"\"$ is maximum at $\"\"$ and minimum at $\"\"$ .

\

The equation $\"\"$ has sine function is symmetricla about the line $\"\"$ .

\

As $\"\"$ increases from $\"\"$ to $\"\"$ , $\"\"$ decreases from $\"\"$ to $\"\"$ .

\

As $\"\"$ increases from $\"\"$ to $\"\"$ , $\"\"$ decreases from $\"\"$ to $\"\"$ .

\

As $\"\"$ increases from $\"\"$ to $\"\"$ , $\"\"$ increases from $\"\"$ to $\"\"$ .

\

As $\"\"$ increases from $\"\"$ to $\"\"$ , $\"\"$ increases from $\"\"$ to $\"\"$ .

\

The cartesian graph with $\"\"$ on the horizontal axis and $\"\"$ on the verticalaxis.

\

The transformation of $\"\"$ with amplitude $\"\"$ , reflected over the $\"\"$ -axis and shifted up by $\"\"$ unit. So $\"\"$ will vary by $\"\"$ from the middle line of $\"\"$ , or between $\"\"$ and $\"\"$ and complete one cycle from $\"\"$ to $\"\"$ , the resulting curve is limcon curve with inner loop.

\

Graph the polar eqation:

\

$\"\"$

\

$\"\"$

\

Graph of the polar equation in cartesian plane $\"\"$ is

\

$\"\"$