Hyperbolic Definition and 336 Threads

Hey guys, I was doing some work on hyperbolic functions and teaching myself to solve some equations. One of the questions in the book really has me stumped: Express using exponential definitions of cosh(x) and sinh(x) find the exact solution of: tanh(x) + sinh(x) = 3 I had a go at...

Homework Statement Hello, Thanks for taking some time to help me out...and I have to apologize for posting a graphic of my logic and attempted answer instead of using LateX (It would take me a very long time just to get this problem viewable) Please help me check my work and logic...

I am a bit confused over the shape of matterless spacetime:confused:: on one side Minkowski space is described as hyperbolic, and deSitter space is (hyper)spherical. Both are used, yet how can you have spacetime being both hyperbolic and spherical?

Homework Statement Limit of x2cosh(1/x) as x approaches 0 Homework Equations The Attempt at a Solution I did some algebra,made into the form infinity over infinity and used hopital's rule. I got limit x2e^(1/x). Then I again made into the form infinity over infinity(by making it 1/x2). Then...

Given a triangle on a hyperbolic surface with all angles and edge length known the area is given by R^2 x(PI - a - b - c), where a, b and c are the angles and R is the radius of curvature of the surface. What if you don't know R? Same question for a triangle on a spherical surface where R is...

A train is traveling at the speed of a bullet. A man, stood on top of the train, fire's a gun in the direction from which the train has come from. (facing rearward) He pulls the trigger the instant the train passes station 'A'. The velocity of the bullet relative to the ground is 0 To an...

Hyperbolic and Inverse Trigonometric Functions How extensive is the use of hyperbolic and inverse trigonometric functions in upper-level calculus and mathematics? I've taken 3 semesters of calculus, and not one of my teachers has gone over hyperbolic functions, and barely touched on inverse...

Is there a general way of writing the Lorentz transformation for (2+1) dimension or higher, in terms of its hyperbolic angle, sinh and cosh ?

If this is in the wrong section, I apologize. I've been doing some independent research on the applications of hyperbolic geometry, and I ve hit a rather difficult snag. I've seen in a few places on line that Mercury's orbit can be more accurately calculated using hyperbolic geometry as...

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...

Hello, I would like to do some stuff with modeling geometry in hyperbolic space in software. When I look up information on hyperbolic space, however, I tend to find only information on working with models of hyperbolic space. For example I find lots of information on the poincare disc model...

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 Prove that: (1+tanhx)/(1-tanhx)=e^(2x) Homework Equations The Attempt at a Solution I tried substituting tanhx for (e^x-e^(-x))/(e^x+e^(-x)) and for (e^(2x)-1)/(e^(2x)+1)) But I really have no clue how to continue...

Homework Statement Evaluate: \int\\{1}/{\sqrt{x^2-1}} dx between -3, -2 I know I'm supposed to use hyperbolic substitution in the question. Homework Equations edit: cosh^2(t) - sinh^2(t) = 1 The Attempt at a Solution let x = -cosht, inside the integral let dx = sinh(t) dt int (...

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...

I like to learn some basic hyperbolic geometry! Starting with the hyperbolic plane, the upper half plane with the hyperbolic lines being all half-lines perpendicular to the x-axis, together with all semi-circles with center on the x-axis. Why and how are there always infinitely many...

Homework Statement What energy (in eV) should a beam of electrons have so that 0.1% of them are able to tunnel through a barrier of height 7.0eV and 1.0 nm wide? Start with the equation for T(E) and set it up with 1/T(E) on one side and let E/U=x for the unknown. Solve the equation for x and...

the questions below for scientific debate 1.how to understand SL(2,R)/SO(2,r)=H^2(2-dim hyperbolic space) 2.Let M be a compact manifold ,T compact lie group,what can we say about M^T(the set of fixed points of M under the action of T),is M^T manifold? how to argue?further,if T is torus,and M is...

\equivHomework Statement Hi, I've been given a hyperbolic identity to prove: 2sinhAsinhB \equiv Cosh(A+B) - Cosh(A-B) Homework Equations Cos(A\pm B) \equiv CosACosB \mp SinASinB The Attempt at a Solution I have Cosh(A+B) and - Cosh(A-B) so i can kind of see that there will be...

I recently came across a problem where I was able to show that \sum_{n=1}^{\infty} \frac{(-1)^n}{n} \tanh \left( \frac{n \pi}{2} \right)=\frac{\ln 2- \pi}{4} through numerical approximation...However, I don't have much practice evaluating such summations analytically, and I was wondering if...

Hi all, I have to rewrite a serie into a fraction of hyperbolic sine but I am lost... My problem looks like this \Sigma_{n=0}^{\infty} exp(K*F)*exp(-F*B(n+0.5)) which can be rearranged into exp(K*F)/(sinh(FB/2) my problem is I cannot relate the serie...

Homework Statement Prove that the magnitude of the impact parameter B equals the length (-b) of the hyperbolic semiminor axis. Homework Equations |B|=|b|=|a|sqrt(e^2-1) The Attempt at a Solution I really don't know where to start. I was thinking of finding a relation between a...

I hope this is the right place to ask this question. Imagine a right triangle with vertices A,B and C and corresponding opposite sides a, b and c such that there is a right angle at B and side b is the hypontenuse. Let the length of side b = 1. If I label side a as sin(A) and side c as...

This is not homework. I've been analysing some space-time diagrams and found I need to know the biggest angle in the illustrated triangle in terms of the lengths and the angle A which are known. I found the equivalent of the cosine rule of Euclidean space for the hyperbolic plane but I'm...

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...

The question is as follows (by the way I'm asking here, cause the calculus and beyond forum seems to be primarily concerned with Calculus,DE, LA and AA): let f(z)=(2z+1)/(z+1) be an isometry of the hyperbolic plane H={z| Im(z)>0}. let l be a hyperbolic line in H which is invariatn under f...

I have this question which is rather simple, basically reiterating a general theorem. Show that S={z in H||z-i|=3/5} is a hyperbolic circle S={w in H| p(w,w0)=r} for r>0 and find sinh(r/2) and w0. Now to show that it's hyperbolic is the easy task, I just want to see if I got my...

Let b>a>0 real numbers, and z a point in H={z in CU{infinity}| Im(z)>0} let I be in H, a euclidean interval which connects az with bz. find the point w in I such that it divides I into two intervals with the same hyperbolic length. Now what I did is as follows: let f be a mobius...

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...

Hello, Given the three maps x_{n+1}=Ax_n with A_1=\begin{pmatrix} 1&-1\\1&1 \end{pmatrix}, A_2=\begin{pmatrix} 1/2&1/2\\-1&1 \end{pmatrix}, A_3=\begin{pmatrix} 3&2\\5/2&2 \end{pmatrix}, describe the dynamics, and say whether or not the dynamics is hyperbolic. Finding eigenvalues...

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...

[SOLVED] find d/dx of hyperbolic function Homework Statement Find: http://www.mcp-server.com/~lush/shillmud/1.1A.Q.JPG Homework Equations d/dx f(x)*g(x) = f(x) * d/dx g(x) + g(x) * d/dx f(x) d/dx f(g(x)) = d/dx f(g(x))* d/dx g(x) d/dx sinh x = cosh x d/dx cosh x = sinh x The...

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...

Homework Statement (I haven't got the thing to write equations so this is a little difficult to understand sorry!) Show that the integral of (4x^2 - 1)^-1/2 from 0.625 to 1.3 is equal to 1/2(ln 5 - ln 2) Homework Equations my formula book states: the integral of (x^2 - a^2)^-1/2 is...

Homework Statement Show that: (I don't have any way of showing it properly so have written it in words) 'The integral from 5 to 3 of (sq root (x^2 - 9) ) with respect to x' = 10 - (9/2) * ln 3 I hope that makes sense! Homework Equations Well I'm not sure.. I *think* that the fact the...

i have a problem in my engineering maths which says as follows: show that if z is a complex number then 2 cos (x) = z + 1 / z and 2 j sin (x) = z - 1/z given that cosh (jy) = cos (y) and sinh (jy) = j sin(y) I can solve the problem without using the hyperbolics but that last...

Hyperbolic Kick, Why is happens?? Homework Statement Why does an object in a hyperbolic orbit passing close to a planet (which is in orbit about another large object like the Sun) get a velocity "kick" from it? Why does it not work for a stationary planet? I think it has to do with...

Homework Statement Determine whether the series converges and diverges. \sum_{n=3}^{\infty}\ln \left(\frac{\cosh \frac{\pi}{n}}{\cos \frac{\pi}{n}}\right) The Attempt at a Solution \sum_{n=3}^{\infty}\ln...

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...

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...

Homework Statement \int \!\sqrt {1+{v}^{2}}{dv} Homework Equations Maple tells me that I have to throw in an arcsinh into the solution some how. The Attempt at a Solution I've tried substituting with tan(x) but that got me no where and from the solution I'm given: 1/2\,v\sqrt...

Homework Statement Evaluate the integral: (int sign) Sech³xTanhx dxHomework Equations Derivative of Sechx = -(SechxTanhx)The Attempt at a Solution Rewrite as: Sech²xSechxTanhx U=sechx Du = -(SechxTanhx)dx -Du = SechxTanhx dx replace into integral -(integral sign) U²du Evaluate: -U³ / 3...

Homework Statement Prove the identity: Cosh(x) + Cosh(y) = 2Cosh[(x+y)/2]Cosh[(x-y)/2] Homework Equations Cosine sum-to-product http://library.thinkquest.org/17119/media/3_507.gif The Attempt at a Solution Can you use the same formula for Cosine sum to product for hyperbolic...