My Math Forum  

Go Back   My Math Forum > High School Math Forum > Algebra

Algebra Pre-Algebra and Basic Algebra Math Forum

Thanks Tree1Thanks
  • 1 Post By skipjack
LinkBack Thread Tools Display Modes
October 21st, 2016, 04:38 AM   #1
Joined: Mar 2015
From: uk

Posts: 33
Thanks: 1

solve hyperbolic equation

Find all real solutions of

4sinh4x - 17sinh3x + 4sinh2x = 0

This is a worked example in my text book. The working says it's possible to combine two of the hyerbolic sines together using an identity to get

4(2sinh3x.coshx) - 17sinh3x = 0

So sinh4x + sinh2x = 2sinh3x.coshx

I can't see how to do this, the book doesn't show the steps. Can anyone show me how it's done and/or which identity to use?

wirewolf is offline  
October 21st, 2016, 05:43 AM   #2
Global Moderator
Joined: Dec 2006

Posts: 20,757
Thanks: 2138

Below are various standard identities for the hyperbolic functions. The first one will help you (by using A = 4x and B = 2x). There are many more (not just ones listed below), corresponding to the various trigonometric function identities.

sinh(A) + sinh(B) ≡ 2sinh((A + B)/2)cosh((A - B)/2)
cosh(A) + cosh(B) ≡ 2cosh((A + B)/2)cosh((A - B)/2)
sinh (A + B) ≡ sinh(A)cosh(B) + cosh(A)sinh(B)
sinh (A - B) ≡ sinh(A)cosh(B) - cosh(A)sinh(B)
cosh (A + B) ≡ cosh(A)cosh(B) + sinh(A)sinh(B)
cosh (A - B) ≡ cosh(A)cosh(B) - sinh(A)sinh(B)
Thanks from wirewolf
skipjack is offline  

  My Math Forum > High School Math Forum > Algebra

equation, hyperbolic, hyperebolic, solve

Search tags for this page
Click on a term to search for related topics.
Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
Solving hyperbolic cosine equation (catenary curve) willmac Trigonometry 0 May 26th, 2011 12:55 PM
Proving that the first order wave equation is hyperbolic demonwolf Applied Math 0 December 12th, 2009 03:19 PM
Numerically solve Hyperbolic case nonlinear PDE Vashuta Applied Math 0 December 6th, 2009 12:55 PM
Help! How to solve the equation? liuyelu Linear Algebra 0 May 21st, 2009 01:05 AM
trig/hyperbolic equation with complex logarithm ekito Complex Analysis 2 March 17th, 2009 08:21 PM

Copyright © 2019 My Math Forum. All rights reserved.