$\"\"$

The polar equation is $\"\"$ .

The equation of the polar curve is a cardiod and it is symmetric about $\"\"$ axis.

Find the top half in the inertval $\"\"$ , multiply the result by 2.

$\"\"$ .

Apply derivative on each side with respect to $\"\"$ .

$\"\"$

$\"\"$ .

Arc length :

The length of a curve with polar equation $\"\"$ is

$\"\"$ .

Substitute $\"\"$ and $\"\"$ in above equation.

$\"\"$

$\"\"$ .

The exact length of curve is $\"\"$ .

$\"\"$

The exact length of curve $\"\"$ is $\"\"$ units.