Rational Points on Graph of Sine Function

Theorem

Consider the graph of the sine function in the real Cartesian plane $\R^2$:

$f := \set {\tuple {x, y} \in \R^2: y = \sin x}$


The only rational point of $f$ is $\tuple {0, 0}$.


Proof


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Sources

  • 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {B}.17$: More About Irrational Numbers. $\pi$ is Irrational
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