# Zeroes of Sine and Cosine/Sine

(Redirected from Zeroes of Sine)

## Theorem

Let $x \in \R$.

$\sin x = 0$, if and only if $x = n \pi$ for some $n \in \Z$.

## Proof

$\sin x$ is:

strictly positive on the interval $\openint 0 \pi$

and:

strictly negative on the interval $\openint \pi {2 \pi}$

The result follows directly from Sine and Cosine are Periodic on Reals.

$\blacksquare$