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If we know that $\sin(n^\circ)$ is constructible where $n$ is some integer,then is $\sin((an)^\circ)$ also constructible for any integer $a$ ?

I am thinking it should be but not sure how to show it? Maybe using some recurrence relation for sin, to express it entirely in terms of powers of $\sin(n^\circ)$?

Got it!

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    (Incidentally, I would just use '$\sin(x)$' rather than '$\sin(n^\circ)$'; the latter is a bit of a red herring since there are constructable values $\sin(x)$ where $x$ isn't a whole number of degrees. There's nothing in the proof that uses the fact that $n$ is an integer.)2012-12-07

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