Complex sine and cosine

Summary

The complex sine and cosine extend the real sine and cosine to all of $\mathbb{C}$ with the formulas $\sin z = (e^{iz} - e^{-iz})/(2i)$ and $\cos z = (e^{iz} + e^{-iz})/2$, see the definition. They are entire functions, and they are not bounded on $\mathbb{C}$.