How to write this expression in terms of a Hyperbolic function?

  • #1
255
8
Homework Statement
How to write this expression in terms of a Hyperbolic function
Relevant Equations
How to write :

##
Eq= e^{t ( -h \pm \sqrt{ x} )}
##

I terms of ##Cosh (x) = e^x + e^{-x} /2 ##
The eqution can be written as:

##
Eq= e^{t( -h + \sqrt{ x} )} + e^{t( -h -\sqrt{ x} )}
##

Can this be written in terms of Cosh x ?
 
Physics news on Phys.org
  • #2
It could be written in terms of ##\cosh \sqrt x##.
 
  • #3
PeroK said:
It could be written in terms of ##\cosh \sqrt x##.
So can it written as:

## Eq = e^{ -ht} ( e^{t\sqrt{x}} + e^{-t\sqrt{x}} ) = 2 e^{ -ht} Cosh ( t \sqrt{x}) ##?
 
Last edited:
  • #4
Safinaz said:
How to write :
##Eq= e^{t ( -h \pm \sqrt{ x} )}##
I presume that represents 2 different 'equations':
##f(t,h,x)= e^{t ( -h + \sqrt{ x} )}## and
##g(t,h,x)= e^{t ( -h - \sqrt{ x} )}##

Safinaz said:
##Cosh (x) = e^x + e^{-x} /2 ##
You are missing brackets and should use a lower case c for ##\cosh##.

Safinaz said:
The eqution can be written as:
##Eq= e^{t( -h + \sqrt{ x} )} + e^{t( -h -\sqrt{ x} )}##
Looks like you are trying to express the two differnt equations as a single equation. That sounds wrong to me. It's a bit like saying ##x = 1 \pm \sqrt 2## and then considering the value of ##(1+\sqrt 2) + (1 -\sqrt 2)## (which is ##2##). It doesn't work.
 
  • #5
Safinaz said:
Can you please write the formula?
It's fairly obvious. I thought the question was to relate that to ##\cosh x##, which I don't think can be simply done.
 
Last edited:
  • Like
Likes Safinaz
  • #6
$$2e^{-ht}=\cosh{ht}-\sinh{ht}$$
 
  • Like
Likes SammyS
  • #7
Safinaz said:
Homework Statement: How to write this expression in terms of a Hyperbolic function
Relevant Equations: How to write :

##
Eq= e^{t ( -h \pm \sqrt{ x} )}
##

I terms of ##Cosh (x) = e^x + e^{-x} /2 ##

Is this the question as given to you, or does it represent where you got to in answering some other question? If the latter, please state the original question.
 

Similar threads

Replies
1
Views
722
  • Introductory Physics Homework Help
Replies
34
Views
471
  • Calculus and Beyond Homework Help
Replies
3
Views
471
  • Calculus and Beyond Homework Help
Replies
1
Views
677
Replies
5
Views
302
  • Introductory Physics Homework Help
Replies
2
Views
369
  • Introductory Physics Homework Help
Replies
8
Views
454
  • Introductory Physics Homework Help
Replies
4
Views
60
  • Introductory Physics Homework Help
Replies
3
Views
271
  • Differential Equations
Replies
10
Views
1K
Back
Top