https://www.youtube.com/watch?v=zd3RyRk6wYI
On Khan Academy, Sal derives the hyperbolic function of sin in terms of $i\theta$. My question is, how did he get rid of the $i$ in the denominator? I know he substitutes $x$ in for $i\theta$, but I still don't understand how he got rid of the $i$ in the denominator.
I tried justifying his math but I just don't understand how that imaginary number is removed. Could someone justify his math? Thank you.
He is just defining the functions that way. He is not deriving them from the normal $\sin$ and $\cos $ functions, although granted it looks a little confusing with the arrows. The arrows are just to indicate that he defines $\sinh$ and $\cosh$ analogously to $\sin$ and $\cos$ respectively.