Hyperbolic functions Definition and 81 Threads

I read the wiki on hyperbolic functions but i don't really understand. I also plotted cosht,sinht on wolfram it made sideways v lying on the x axis. Can anyone explain why people made hyperbolic functions. I still don't really understand what it means apart from cosht being the x coordinate...

Hello All, Am studying GR using a text by Hartle. From time to time need a better intuitive understanding of hyperbolic functions than I currently have. Never learned them for my physics undergrad. Any short sweet highly understandable primer, etc, that anyone knows of (preferably free of...

Homework Statement I need to solve: 1/4tanh(θ) + c Homework Equations x=2sinh(θ) θ = arcsinh(x/2) The Attempt at a Solution I worked out that since tanh(θ) = sin(θ)/cosh(θ) then 1/4tanh(θ) + c = x/8cosh(θ) + c But i don't know how to work out cosh(θ) or cosh(arcsinh(x/2))...

Homework Statement find all other hyperbolic function at x for tanhx=12/13 Homework Equations tanhx = sinhx/coshx cothx=1/tanhx etc... The Attempt at a Solution the only thing i got is cothx=13/12 all i need to know is how to find sinhx and i will be fine.

Homework Statement $\displaystyle \Large y = \ln (x + \sqrt{x^2 - 1})$ Homework Equations The Attempt at a Solution i used my graphing calc.. but that's not the point. how do i do this question? i mean, how do i find the graph of that function?

Homework Statement Find the real part, the imaginary part, and the absolute value of: cosh(2-3i) Homework Equations The Attempt at a Solution I know how to write this using exponentials, but when I looked up the answer the book expanded cosh(2-3i) to cosh 2 cos 3 − i sinh 2...

y=km(ln(cosh(gt/km)^(1/2))) constants k and m dy/dx=gtanh((gt/km)^(1/2))/(2(gt/km)^(1/2))...?

Find the points on the graph of y=sinhx at which the tangent line has slope 2 dy/dx=coshx=2 (e^x+e^(-x))=4 x-x=ln4

Given the quantity Cosh(x)*Cosh(y) where x and y are two indipendent real variables is it possible to write it only in function of k=Cosech(x)*Cosech(y) ? It could seem a quite easy problem but I spent a few days between the proprieties of hyperbolic functions and I really...

Orthogonality Property of Hyperbolic functions ? Hi all, I have seen Orthogonal property for trigonomeric functions but I am unsure if there is something similar for sinh() , cosh() ? . I know that the integral of inner product of the two functions should be zero for them to be...

1. I am asked to calculate \int \frac{dx}{cosh(x)} 2. Homework Equations 3. The Attempt at a Solution I know that \frac{1}{cosh(x)} is equivalent to "sech(x)" which by definition is \frac{2}{e^x+e^{-x}}. I'm confused & I don't know which one I need to use for this question...

Homework Statement If sinhx=tany show x=ln(tany±secy) Homework Equations sinhx=0.5(e^x-e^(-x)) secy=1/cosy cosy=0.5(e^y+e^(-y)) tany=(e^(jx)-e^(-jx))/(e^(jx)+e^(-jx)) tany=siny/cosy The Attempt at a Solution 0.5e^x -0.5e^-x=tany 0.5e^(2x) -0.5=tany e^x e^(2x) -2tany e^x -1 = 0...

Homework Statement Question(1) : Find the Cartesian equation of Re[ z - i / z + 1 ] = 0. If the locus is a circle, give its radius and the coordinates of its center. The Attempt at a Solution Workings : So I attempted to solve the problem and my workings are as below ... Since Re = Real...

Homework Statement power series expansion of: ((cosh x)/(sinh x)) - (1/x) Homework Equations cosh x = (1/2)(ex + e-x) sinh x = (1/2)(ex - e-x) The Attempt at a Solution what i have so far: I simplified the first part of the eq to read : e2x-1 e2x-1 now I am stuck...

Homework Statement I don't understand how to take the derivative of inverse hyperbolic functions such as sinh^{-1}(x). I know that the derivative of sinh(x) is cosh(x) but don't know what to do with the inverse. Homework Equations The Attempt at a Solution I'm completely at a...

integrate (x^2) / (4+x^2)^(3/2) Im not allowed to apply hyperbolic functions to this and have been trying to solve applying to a 90 deg. angle. x = 2tan(theta) x^2 = 4tan^2(theta) dx = 2 sec^2(theta) Hopefully you can se where I am going with this (trigonomic substitution) Im...

I have a picture of a problem and the answer. But a place in the answer I can't understand how they get from one function to the next, could you guys please explain it? I have marked it in red? http://img381.imageshack.us/img381/1839/hyperik2.png

Homework Statement Find the derivative of y=ln(cosh(2x^3)) The attempt at a solution is this the same as saying (1/(cosh(2x^3)) ? The correct answer is 6x^2 - ((12x^2)/(e^4x^3 + 1))... how do you derive this? I am really stuck on this question I didn't learn about hyperbolic functions in...

Homework Statement Given the trigonometric identity cos(x+y)... use Osborn's rule to write down the corresponding identity for cosh(x+y)... Use the definitionis of the hyperbolic functions to prove this identity Homework Equations The Attempt at a Solution I can use Osborns rule...

[SOLVED] Mathematica does not like hyperbolic functions So, consider the equation cosh(x)=n*x For a given n, the equation has 0, 1, or 2 possible values of x. If n is below the critical value, the equation has no solutions. If n is above the critical value, the equation has two solutions...

[SOLVED] Hyperbolic functions As part of a long winded "show that" question I've ended up at the point where I have xcothx and I want to show that this is equal to cothx - \frac{1}{x} only I have no ideas how to get there. I can't see any reason why this should be so, but I'm pretty confident...

Homework Statement a) Find y' if y = x^2arcsinh(2x) b) Find y' if y = xarctanh(x) + ln[(1-x^2)^1/2] c) Find y' if y = arccoth[sqrt(x^2+4)] Homework Equations d/dx arcsinh(x) = 1/sqrt(1+x^2) d/dx arctan(x) = 1/(1-x^2) d/dx arccoth(x) = 1/(1-x^2) The Attempt at a Solution I am still...

I was just browsing through my textbook in the section on hyperbolic trig functions. It defines sinhx to be \frac{e^x-e^{-x}}{2}, which comes from breaking the function f(x)=e^x into two functions, the other of which forms coshx. Oddly enough, this is one of the only sections in the text that...

Homework Statement The Saint Louis arch can be approximated by using a function of the form y=bcosh(x/a). Putting the origin on the ground in the center of the arch and the y-axis upward, find an approximate equation for the arch given the dimenson shown in the figure(attachment). In other...

The hyperbolic functions are defined as follows: coshz = e^{z} + e^{-z} /2 sinhz = e^{z} - e^{-z} /2 a.)Show that coshz = cos (iz). What is the corresponding relationship for sinhz? b.)What are the derivatives of coshz and sinhz? What about their integrals? c.)Show that cosh^2z - sin^2 =1...

Cosh u = (2sinh u) -1 Working from definitions http://img118.imageshack.us/img118/3271/eusm4.png Its a worked example from the book, which isn't very well explained. The only step i struggle on is from how the managed to get all the u's positive (step 2). I plugged some numbers in for u and...

Anyone know of a good unit or introduction online to hyperbolic trig functions which would be good for a pre-calculus level class? Is it worth at least introducing hyperbolic functions to pre-calculus students? I'm ahead of where I'm normally at this time of year in pre-calc, and thought...

I wonder how I can compute hyperbolic terms like cosh(ln2). The calculator we're allowed to use doesn't have buttons for calculating hyperbolic functions.

Just want to check my answer. Find the equation of the tangent to the curve y^3 + x^2 \cosh y + \sinh^3 x = 8 at the point (0, 2) I firstly found the derivative and the gradient of the curve at point (0, 2) 3y^2 \cdot \frac{dy}{dx} + x \cosh y + x^2 \sinh y \cdot \frac{dy}{dx} + 3 \sinh^3 x...

Hi! How do you write the LaTeX code for the secant, cosecant, and cotangent hyperbolic functions? I tried using \sech, \csch, and \coth but I am getting an error when I run the latex program. It is giving me a undefiend control sequence message? Is there a package I need to include in my .tex...

I am having trouble solving for x 24 cosh x + 16 sinh x = 2500 do I multiply out all the (e)s?