# What is the arclength of the polar curve #f(theta) = csc^2theta-cot^2theta # over #theta in [pi/3,pi/2] #?

##### 1 Answer

#### Answer:

Hi there!

Let's start off with the formula for the arc length of a polar curve whereby:

#### Explanation:

First of all, it's important to note that

Notice anything about this function? A trig identity perhaps?

Well,

Therefore, this function would simplify down to r = 1! This makes everything much easier!

Substituting everything into the formula we get:

Simplifying everything:

Integrating a **constant** with respect to theta we get:

Now substitute the bounds in:

Therefore, the arclength of the polar curve is

Hopefully everything was clear and concise! If you have any questions, feel free to ask! :)