# Why are $sin(x)$ and $cos(x)$ irrational for (non-zero) rational values of $x$? [duplicate]

$$sin(x)$$ is the ratio between two sides of a triangle. One or more sides must be irrational for $$sin(x)$$ to be irrational. Why does a rational value of $$x$$ guarantee this?
• @anomaly It shouldn't be marked as a duplicate of that one. The answers there only establish weaker results characterizing the rational multiples of $\pi$ that give rational outputs, but not irrationality of outputs for rational inputs, – logarithm May 10 at 23:29