# Absolute value of $\sin z$ on square

Show that $|\sin z|\geq 1$ at all points on the square with vertices $\pm (N+1/2)\pi\pm(N+1/2)\pi i$, for any positive integer $N$.

-

## 1 Answer

Hint: $|\sinh(y)| = |e^{y} - e^{-y}|/2 >1$ if $|y| > \ln(1 + \sqrt{2})$.

-