Question

How to you turn a number into an answer with pi in it?

I'm very sorry in advance that I do not have the vocabulary to ask this question in the most concise way possible. If I did know all the correct terminology I might have been able to google my question, but here I am instead! What I am trying to learn how to do better is inputting integrals into a TI-84 Plus graphing calculator. I am currently entering `int_0^(pi/4)(cos2theta)^2(d theta)` into the calculator, with the answer "0.3926990817", which I understand is correct. So that's cool. I also know from typing the same integral in to an online calculator that this number is the same as `pi/8`, but I only know that because I was able to type it into an online calculator, which I obviously won't be able to use during tests or quizzes. So my question is, how would I convert that decimal number my graphing calculator gave me into `pi/8` using the calculator?

Note: Also, if there happen to be any tips that compliment the answer to my above question regarding solving double or triple integrals using a graphing calculator would be greatly appreciated!

Thank you in advance!

Answer 1

Yes, `pi/8 approx 0.3926990817`
See below.

Explanation:

Here your calculator gave you the result `0.3926990817`

To make this value an approximate product of `pi` simply divide the result by `pi` - If your calculator does not have a key for `pi` use `3.14159265`

In your example `0.3926990817 div 3.14159265 = 0.12500000014323945 approx 0.125`

Now notice that `1/0.125 = 8`

Hence, `pi/8 approx 0.3926990817`

Hope this helps.