Zeroes of Sine and Cosine/Sine
< Zeroes of Sine and Cosine(Redirected from Zeroes of Sine)
Jump to navigation
Jump to search
Theorem
Let $x \in \R$.
- $\sin x = 0$, if and only if $x = n \pi$ for some $n \in \Z$.
Proof
From Sine and Cosine are Periodic on Reals: Corollary:
$\sin x$ 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.
$\blacksquare$