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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.

Matthew Leingang
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oiajfioeaew
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1 Answers1

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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.

M47145
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