Question

How do you get the arc length of the polar curve?

it's of an entire circle r = 2acos(theta)

Answer 1

Step 1:

The polar curve is .

The region bounded by the curve is 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 .