Rational Points on Graph of Cosine Function

Theorem

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

$f := \left\{ {\left({x, y}\right) \in \R^2: y = \cos x}\right\}$

The only rational point of $f$ is $\left({0, 1}\right)$.

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