# Pi is Irrational/Proof 3

## Proof

From Rational Points on Graph of Sine Function, the only rational point on the graph of the sine function in the real Cartesian plane $\R^2$:

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

is the point $\left({0, 0}\right)$.

But $\left({\pi, 0}\right)$ is also on $f$.

Hence $\pi$ cannot be rational.

$\blacksquare$