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Niven's theorem says that if $\theta$ is a rational multiple of $\pi$ and $\sin \theta$ is rational then $\sin \theta = 0, -\frac12, \frac12, -1, 1$. But is this theorem applicable to cosine function?

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Hint: What is the relationship between cosine and sine? – Hayden Aug 12 '14 at 17:48
up vote 7 down vote accepted

Yes because $\cos\theta=\sin(\frac\pi 2-\theta)$.

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Yes. Use fundamental formula $sin^2(x)+cos^2(x)=1$ or trigonometric circle and you can just change sin with cos and viceversa.Think that $sin (x)= cos (\frac{\pi}{2}-x)$ and $cos(x)=sin (\frac{\pi}{2}-x)$.

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