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Possible Duplicate:
When is $\sin(x)$ rational?

Let $m \in \mathbb Z, m\geq1$, then $\cos(2 \pi/m) \in \mathbb Q$ if and only if $m \in \{1,2,3,4,6\}$.

Why is this statement true? Why is $\cos(2 \pi/m)$ always non rational for the integer $m >6$?

Thanks very much.

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    I wonder if there is a Galois theoretic explanation of this? Something to do with cyclotomic extensions of $\mathbb{Q}$?2012-10-13

1 Answers 1