1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Hyperbolic Trig Inverses

  1. Dec 3, 2006 #1
    I need to determine an algebraic form for arcsech(x) = ?

    So far what I've come up with is as follows:

    y = \frac{2}{{e^x + e^{ - x} }} \\

    y = \frac{2}{{e^x + e^{ - x} }}\left( {\frac{{e^x }}{{e^x }}} \right) \\

    y = \frac{{2e^x }}{{e^{2x} + 1}} \\

    ye^{2x} - 2e^x + y = 0 \\

    Need to continue solving for x, thanks for any suggestions.
    Last edited: Dec 3, 2006
  2. jcsd
  3. Dec 3, 2006 #2


    User Avatar
    Science Advisor

    Let z= e2x and you equation becomes
    [itex]yz^2- 2z+ y= 0[/itex]
    Use the quadratic formula to solve for z and then 2x= ln z.
  4. Dec 3, 2006 #3


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    Set [itex]u=e^{x}[/itex]
    Thus, you get the equation in u:


    1.Can you solve that for u, remembering that u>0?
    2. Solve afterwards for x!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook