Rational multiples of $\pi/2$ whose sines are also rational

Asked Jan 10 '13 at 12:46

Active Jan 10 '13 at 13:12

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Let $f(x)=\sin(x\frac{\pi}{2})$. Let $R$ the set of $x$ such that :

Hence, $0\in R$ as $f(0)=0$. $1\in R$ as f(1)=1. And $\frac{1}{3}\in R$ as $f(\frac{1}{3})=\frac{1}{2}$.

Are they any other elements of $R$ ? How to find them all ?

Thanks !

edited Jan 10 '13 at 13:12

Andrew Uzzell

asked Jan 10 '13 at 12:46

Xoff

2

http://en.wikipedia.org/wiki/Niven%27s_theorem – Hans Lundmark Jan 10 '13 at 15:23
1

Related: http://math.stackexchange.com/questions/15823/sine-values-being-rational – Hans Lundmark Jan 10 '13 at 15:25
Is there a proof of Niven's theorem? I can't seem to find it on any of those sites or links... – Adam Rubinson Jan 10 '13 at 15:58
Actually there is a Proof Sketch in the "Talk" section of the wikipedia article. Thanks – Adam Rubinson Jan 10 '13 at 16:28

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