$\"\"$

\

The polar curve is $\"\"$ .

\

The equations of the graphs are $\"\"$ and $\"\"$ .

\

The periodicity of the curve $\"\"$ is $\"\"$ .

\

Graph:

\

Graph the curves $\"\"$ , $\"\"$ and $\"\"$ on $\"\"$ .

\

$\"\"$

\

Observe the graph,

\

The green and pink curves are anti-clockwise rotational curves of $\"\"$ by the angles $\"\"$ and $\"\"$ respectively.

\

Therefore, $\"\"$ and $\"\"$ are counter-clockwise rotational graphs of

\

$\"\"$

\

$\"\"$

\

In general the $\"\"$ is the anticlockwise rotational graph of $\"\"$ by an angle $\"\"$ .

\

$\"\"$

\

$\"\"$ and $\"\"$ are counter-clockwise rotational graphs of $\"\"$ .

\

In general the $\"\"$ is the anticlockwise rotational graph of $\"\"$ by the angle $\"\"$ .