Is [math]pi/arctan(4/3)[/math] rational? Post proof.

>>8581652
You see that little preview LaTeX button? Use it. Also, the homework board is

>>>/hm/

>>8581652
What I meant to write is [math]\frac{\pi}{arctan(\frac{4}{3})}[/math]

Fucking latex

>>8581658
Fuck off, its a math question and Wolfram doesnt have an answer to it. Google doesnt bring up any answers.
Im fucking curious, you arrogant shit

If pi/arctan(3/4) then it can be expressed as some a/b where a and b are whole numbers

Not possible

QED

>>8581669
>Not possible
But how can you prove that?
[math]arctan(\frac{4}{3})[/math] might just be expressable by some [math]\frac{a*pi}{b}[/math] where a and b are whole numbers...

>>8581750
lol Americans...

>>8581750
Let [math]p\pi \in \mathbb{Q}[/math] with [math]0 \neq p \in \mathbb{Q}[/math].
Then [math]p^{-1}p\pi=\pi \in \mathbb{Q}[/math].

>>8581774
that's completely retarded. p= 2/pi

>>8581774
>>8581810
This shit is both retarded and irrelevant. He's asking if [math] \arctan \frac{4}{3} [/math] is a rational multiple of [math] \pi [/math].

>>8581810
>p= 2/pi
How do you know that [math]2/\pi[/math] is rational you moron?
Mine is a proof by contradiction that that [math]p\pi[math] is not rational.

>>8581840
Well you've missed the point there. He was trying to say that if you assume that p is rational than the question is trivial (literally exercise 1.1 in Rudin). But you can't just assume that [math] \arctan (4/3) [/math] is rational and then go on to show that [math]p \pi [/math] is rational. And that's what anon was trying to show, that the product of two irrational numbers could still be rational.

File: productsum.jpg (58KB, 605x412px) Image search: [Google]

58KB, 605x412px

>>8581652
Only if arctan(4/3) is irrational. I'm trying to prove that it is irrational but it's 5:30 am where I'm at so I might get too tired to post it. I'll post the proof if I figure it out though

>>8581816
The only guy who gets it... sigh

Anyway, pi/arctan(x) would be rational only for values where arctan(x) is (p/q)*pi with p,q=/=0, for it would equal q/p and thus be rational.
Sorry about the shitty notation, I'll figure out the LaTeX tags after this.
Now arctan(4/3) would roughly mean tan(x) = 4/3 = sin(x)/cos(x) where sin(x) = k*4 and cos(x) = k*3 where 0<k<1.
Simplest case is sin(x)>cos(x) and x = n*pi [ arctan(4/3) IS x) ] so pi/2 > x > pi/4.
Ah fuck, I feel like I'm kind of on the right track but can't follow this anymore. Need a notebook