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.

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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.

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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.

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.

Quote:

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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.

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

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