Step 1:

The polar curve is $\"\"$ .

The curve is a four leaved rose.

Four loops of the rose are determined by substituting $\"\"$ .

$\"\"$

General solution of sine function $\"\"$ is $\"\"$ .

$\"\"$

Substitute $\"\"$ in above expression.

$\"\"$

Arc length of the curve in polar form is $\"\"$ .

Consider $\"\"$ .

Differentiate with respect to $\"\"$ on each side.

$\"\"$

Step 2:

Substitute $\"\"$ , $\"\"$ and limits of $\"\"$ in the arc length formula.

$\"\"$

Solution:

Arc length of the polar curve $\"\"$ is $\"\"$ .