Paul Masson on Nostr: these two functions are special cases of Jacobi elliptic functions: \[ ...

these two functions are special cases of Jacobi elliptic functions:

\[ \operatorname{sl}( z ) = \operatorname{sn}( z | -1 ) \hspace{3em}
\operatorname{cl}( z ) = \operatorname{dn}( z | 2 ) \]

And if you'd like to see visualizations in 3D, here you go:

https://paulmasson.github.io/math/docs/functions/lemniscateSin.html
https://paulmasson.github.io/math/docs/functions/lemniscateCos.html