Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

Noliec

Does anyone know where you could find the deduction of the inverse of tanh(x) starting from the standard hyperbolic trigonometry definitions? (Or does anyone possibly know how to deduce it from them?)

  • 6 months ago
  • 6 months ago

  • This Question is Closed
  1. Noliec
    Best Response
    You've already chosen the best response.
    Medals 2

    @hartnn , @TuringTest , @AravindG Please help ;_;

    • 6 months ago
  2. Noliec
    Best Response
    You've already chosen the best response.
    Medals 2

    I basically get it, down to tanh(x)=(e^(2x)-1)/(e^(2x)+1)

    • 6 months ago
  3. AravindG
    Best Response
    You've already chosen the best response.
    Medals 0

    It is right isnt it?

    • 6 months ago
  4. Noliec
    Best Response
    You've already chosen the best response.
    Medals 2

    Indeed, but how do you go from here to the inverse of tanh(x)?

    • 6 months ago
  5. hartnn
    Best Response
    You've already chosen the best response.
    Medals 1

    do u know componendo - dividendo ?

    • 6 months ago
  6. AravindG
    Best Response
    You've already chosen the best response.
    Medals 0

    Take tanh x=y. Then apply log on both sides.

    • 6 months ago
  7. AravindG
    Best Response
    You've already chosen the best response.
    Medals 0

    Solve for x.

    • 6 months ago
  8. hartnn
    Best Response
    You've already chosen the best response.
    Medals 1

    if a/b = c/d then (a+b) /(a-b) = (c+d)/ (c-d) did u know this ?

    • 6 months ago
  9. Noliec
    Best Response
    You've already chosen the best response.
    Medals 2

    That's what I did, I didn't get anywhere on the log expression though. Hmm, not sure hartnn.

    • 6 months ago
  10. hartnn
    Best Response
    You've already chosen the best response.
    Medals 1

    that rule is called componendo-dividendo apply that for y/1= (e^(2x)-1)/(e^(2x)+1)

    • 6 months ago
  11. Noliec
    Best Response
    You've already chosen the best response.
    Medals 2

    I'd have to give a proof in order to utilize it though. D: It's supposed to be solved without it.

    • 6 months ago
  12. hartnn
    Best Response
    You've already chosen the best response.
    Medals 1

    that will isolate e^2x and hence you can apply log

    • 6 months ago
  13. hartnn
    Best Response
    You've already chosen the best response.
    Medals 1

    solved without what ?

    • 6 months ago
  14. Noliec
    Best Response
    You've already chosen the best response.
    Medals 2

    No shortcuts. :D

    • 6 months ago
  15. Noliec
    Best Response
    You've already chosen the best response.
    Medals 2

    Algebraically

    • 6 months ago
  16. AravindG
    Best Response
    You've already chosen the best response.
    Medals 0

    Great! Good work!

    • 6 months ago
  17. hartnn
    Best Response
    You've already chosen the best response.
    Medals 1

    lol ok, don't apply that rule (bdw, that was algebraic property) y= (e^(2x)-1)/(e^(2x)+1) y (e^2x +1) = e^2x -1 y e^2x + y = e^2x -1 y e^2x -e^2x = -1-y need i go further ?

    • 6 months ago
  18. hartnn
    Best Response
    You've already chosen the best response.
    Medals 1

    hint for next step factor out e^2x from on left side

    • 6 months ago
  19. hartnn
    Best Response
    You've already chosen the best response.
    Medals 1

    but did u get what i did ?

    • 6 months ago
  20. hartnn
    Best Response
    You've already chosen the best response.
    Medals 1

    \(\huge \dfrac{1}{2}\ln (\dfrac{1+x}{1-x})\) you should get this

    • 6 months ago
  21. hartnn
    Best Response
    You've already chosen the best response.
    Medals 1

    -1-y / y-1 = (1+y)/ (1-y) the 1/2 will come outside ln right ? because 2x= ln (...)

    • 6 months ago
  22. Noliec
    Best Response
    You've already chosen the best response.
    Medals 2

    What happens after you apply ln?

    • 6 months ago
  23. hartnn
    Best Response
    You've already chosen the best response.
    Medals 1

    e^2x =[(1+y)/(1-y) ] clear till here ??

    • 6 months ago
  24. Noliec
    Best Response
    You've already chosen the best response.
    Medals 2

    Man I feel stupid. D:

    • 6 months ago
  25. Noliec
    Best Response
    You've already chosen the best response.
    Medals 2

    Absolutely.

    • 6 months ago
  26. hartnn
    Best Response
    You've already chosen the best response.
    Medals 1

    any more doubts?

    • 6 months ago
  27. Noliec
    Best Response
    You've already chosen the best response.
    Medals 2

    Nope, thanks a lot! :)

    • 6 months ago
  28. hartnn
    Best Response
    You've already chosen the best response.
    Medals 1

    welcome ^_^

    • 6 months ago
    • Attachments:

See more questions >>>

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.