---
tag: 00NZKRSWNX
kind: concept
name: Complex sine and cosine
aliases: [complex-sine, complex-cosine]
msc: [33B10]
sources:
  - url: https://en.wikipedia.org/wiki/Sine_and_cosine
    locator: Complex arguments
---

## 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|0A7YDKRNR6]].
They are entire functions, and they are not bounded on $\mathbb{C}$.