Why are these the same, isn’t the hyperbolic functions related to e only ?

Hi u/IdenticalGD,

**You are required to explain your post and show your efforts. _(Rule 1)_**

Please add a comment below explaining your attempt(s) to solve this and what you need help with **specifically**. If some of your work is included in the image or gallery, you may make reference to it as needed. See the sidebar for advice on 'how to ask a good question'. Don't just say you need help with it.

**Failure to follow the rules and explain your post will result in the post being removed**

---

*I am a bot, and this action was performed automatically. Please [contact the moderators of this subreddit](/message/compose/?to=/r/askmath) if you have any questions or concerns.*
They’re called hyperbolic trig functions for a reason, because they map to the unit hyperbolas.
Functions like these satisfy a sort of "parametric" form. Cosh^2 x - Sinh^2 x =1 can also be written compactly as x^2 - y^2 =1 (by substituting x = Coshx and y = Sinhx)

Now, if you solve algebraicly for x as an example, you end up with x = ±sqrt( 1+ y^2 ).
Congrats, you just went from an explicit equation to an implicit form.
cosh^2 t - sinh^2 t = 1
by
cosh^(2)(t)-sinh^(2)(t)=1

Set x=sinh(t), y=cosh(t).

0 like 0 dislike