Finding the average rate of change for h(t) = cot t

Hello everyone!

Here is the problem, I would appreciate some help :)

**Exercise 2.1.3**

Find the average rate of change of the function h(t) = cot(t) over the interval

π/6 -> π/2

I don't have cot on my calculator, so before, when I solved exercises like this one I would first calculate 1/tan. The problem is, tan is undefined for π/2. So, any ideas on what I should do? :)

By the way, is there some easy way to write equations, fractions etc. more neatly on MHF? I really love this forum and would like to be able to ask for help in more neat ways, so it does not become so difficult for everyone to read it.

Re: Finding the average rate of change for h(t) = cot t

Quote:

Originally Posted by

**Nora314** Hello everyone!

Here is the problem, I would appreciate some help :)

**Exercise 2.1.3**

Find the average rate of change of the function h(t) = cot(t) over the interval

π/6 -> π/2

I don't have cot on my calculator, so before, when I solved exercises like this one I would first calculate 1/tan. The problem is, tan is undefined for π/2. So, any ideas on what I should do? :)

By the way, is there some easy way to write equations, fractions etc. more neatly on MHF? I really love this forum and would like to be able to ask for help in more neat ways, so it does not become so difficult for everyone to read it.

It might help if you remember $\displaystyle \displaystyle \begin{align*} \tan{x} = \frac{\sin{x}}{\cos{x}} \end{align*}$, so $\displaystyle \displaystyle \begin{align*} \cot{x} = \frac{1}{\tan{x}} = \frac{\cos{x}}{\sin{x}} \end{align*}$.

To write up the mathematics nicely, we use the inbuilt LaTeX compiler.

Re: Finding the average rate of change for h(t) = cot t

Thank you so much for the help! :) Well, knowing that still made it difficult to find the answer, since sin(π/2) = 0, so the answer would be undefined.

I think I came up with a solution, though, tan(π/2) is infinely small, so I just made it = 0, since this is about finding the "average" rate of change anyways, so there is no need to be too precise, I believe. Anyway, when I did this it gave the right answer from the answer key.

Re: Finding the average rate of change for h(t) = cot t

Quote:

Originally Posted by

**Nora314** Thank you so much for the help! :) Well, knowing that still made it difficult to find the answer, since sin(π/2) = 0, so the answer would be undefined.

I think I came up with a solution, though, tan(π/2) is infinely small, so I just made it = 0, since this is about finding the "average" rate of change anyways, so there is no need to be too precise, I believe. Anyway, when I did this it gave the right answer from the answer key.

No, $\displaystyle \displaystyle \begin{align*} \sin{\frac{\pi}{2}} = 1 \end{align*}$ and $\displaystyle \displaystyle \begin{align*} \cos{\frac{\pi}{2}} = 0 \end{align*}$.

Re: Finding the average rate of change for h(t) = cot t

Ah sorry, of course, you are right! Thank you :)