ITT: We post entrance exam problems from our countries and see if people elsewhere can solve them.
(Kyoto University) Is tan(1°) rational?
>>75225335
damn, if this is not a recurrent problem in your curriculum, that's pretty hard for uni entrance exams, hell I am a stem graduate and can't think of a solution from the top of my head
I assume sine1 and cosine1 get oveflowed in a calculator, if not the solution is trivial
else if I had trig identities ready I'd probably assume its rational and try to reach a known irrational tan
the math part (the rest had to do with memorization) of our exams for uni entrance revolved around basic calculus for what it's worth
>>75225335
I'm sure 6 years ago I knew the answer but don't need to worry about that shit anymore.
>I assume sine1 and cosine1 get oveflowed in a calculator, if not the solution is trivial
No calculator allowed.
>else if I had trig identities ready I'd probably assume its rational and try to reach a known irrational tan
This is the right idea. The rest of the problem isn't that hard.
This was actually taught in my first year at college (biostatistics), it is irrational, I think.
The entrance math problems for my university were based around basic algebra, trigonometry and stadistics, nothing really that difficult.
>>75227896
Why would they teach you that in a bio-statistics class?
>>75225335
Exams here are so easy
I think even american can solve this shit
>>75228637
I've always thought exams in Russia were tough after reading this:
https://arxiv.org/pdf/1110.1556.pdf
>>75227691
This, self employed master race
>>75227959
It wasn't actually part of our curriculum, our teacher just wanted to teach some interesting things about math and shittt
tan(1) is irrational obviously, but how to prove it? wouldnt be able to do that on the spot but given some trigonometric identities (which chinks surely stamped in their heads), you can easily prove by contradiction that tan 1 must be irrational, otherwise some other value of cos or sin would be rational too, which would mean that you could prove certain roots like the square root of 3 is irrational, which is a contradiction.