Hyperbolic Definition and 336 Threads

If the circumference of the region bounded by the curve y=cosh(x) and the lines y=0 x=a and x=-a is 2a+4, where a>0 find the area of the surface obtained by rotating the part of the curve y=cosh(x) between x=a x=-a and around the x axis. This is my homework question.I tried to solve it.I...

Homework Statement I am a little confused on the steps to take to solve these kinds of functions. Solve: cosh z = 2i The Attempt at a Solution We were given identities for sinh z = 0 and cosh z = 0 and also other identities like cosh(z) = cos (iz) So cos (iz) = 2i cos...

Homework Statement \int^4_3 \frac{1}{\sqrt{3x^2-6x+1}}\,.dx The attempt at a solution I complete the square for the quadratic: \sqrt{3x^2-6x+1} \\=\sqrt{3(x^2-2x+\frac{1}{3})} \\=\sqrt 3 \times \sqrt{(x-1)^2-\frac{2}{3}} \int^4_3 \frac{1}{\sqrt{3x^2-6x+1}}\,.dx \\=\frac{1}{\sqrt 3}\int^4_3...

Homework Statement Find \int \frac{x}{\sqrt{2x^2-2x+1}}\,dx The attempt at a solution First, i complete the square for the quadratic expression: 2x^2-2x+1=2((x-\frac{1}{2})^2+\frac{1}{4}) \int \frac{x}{\sqrt{2x^2-2x+1}}\,dx=\int \frac{x}{\sqrt 2 \sqrt{(x-\frac{1}{2})^2+\frac{1}{4}}}\,dx...

Homework Statement If \sinh^{-1}x=2\cosh^{-1}y, prove that x^2=4y^2(y^2-1) The attempt at a solution I re-wrote \sinh^{-1}x and 2\cosh^{-1}y in terms of x and y. \sinh^{-1}x=\ln(x+\sqrt{x^2+1}) \\2\cosh^{-1}y=2\ln(y+\sqrt{y^2-1})=\ln(y+\sqrt{y^2-1})^2...

Is there an easy way to see this? can it be see via the penrose diagram? does it have anything to do with how when a stone is thrown in AdS it will alwayscome backk in finite time..

Bany's question from Yahoo Questions: CB

Homework Statement Find the Riemann function for uxy + xyux = 0, in x + y > 0 u = x, uy = 0, on x+y = 0 Homework Equations The Attempt at a Solution I think the Riemann function, R(x,y;s,n), must satisfy: 0 = Rxy - (xyR)x Rx = 0 on y =n Ry = xyR on x = s R = 1 at (x,y) = (s,n) But I...

Homework Statement Show: sinh(z + i2(pi)) = sinh(z) using sinh(z) = (ez - e-z)/2 Homework Equations The Attempt at a Solution So far I have (ex + i(2∏+y) - e-(x+i(2∏+y))/2. Need help proceeding from here. My thoughts were to define a z' = x + i(2∏+y) but I don't think that I can then say...

integrate Sinh4(x) I have been struggling with this problem for a week. I know the answer because of wolfram but I cannot see how it gets it. Honestly, I can't even decide what to make my substitution as. I haven't really had problems with any other questions from our homework but this one and...

Homework Statement why is the answer not e^10x ? If you ignore the e's it should be 5x - 5x + 5x - - 5x, or 5x - 5x + 5x + 5x, which is 10x

Homework Statement Show that cosh^2(x) = (cosh(2x) - 1)/2 Homework Equations cosh(x) = (e^x + e^-x)/2 The Attempt at a Solution I have attempted this multiple times and get the same results every time. Squaring cosh(x) I get 1/4(e^2x + e^-2x +2), which is i believe 1/4(cosh(2x) +2)...

Hi, I am trying to understand solving boundary valued partial differential equations and it's relation to hyperbolic functions. In one of my problems, there is a PDE and the solution contains the hyperbolic function "cosh". I was just curious if anyone has any information for me to read up on...

Homework Statement If lny = sinh^(-1)(x), prove that (1+ x^2)y'' + xy' - y = 0 The attempt at a solution I have tried various (unsuccessful) ways of doing this, but the basic procedure that I've done is: D.w.r.t.x for lny = sinh^(-1)(x) This gives: (1/y)y' = 1/(1 + x^2) To...

Homework Statement http://s1.ipicture.ru/uploads/20111203/B1Ax1OcU.jpg Frankly, I've been sitting staring at that problem for long enough, and it just can't be solved through the direct use of the standard hyperbolic identities. I need a hint.

Hi! I'm implementing a scheme to solve the following equation \frac{\partial \psi}{\partial t}=-c_{s} \cdot \frac{\partial \phi}{\partial x} \frac{\partial \phi}{\partial t}=-c_{s} \cdot \frac{\partial \psi}{\partial x} c_{s} is just the isothermal velocity of sound. The equations are for a...

I am reading through a worked example of the Taylor series expansion of Sinh(z) about z=j*Pi The example states: sinh(j*Pi)=cos(Pi)*Sinh(0) +jcosh(x)sin(y) I am unsure of this relation. I understand why the x terms are zero but don't know the relation to expand sinh. Can anyone shed...

Homework Statement ∫5/(4x√(9-16x2)dx Homework Equations I am pretty sure this is in the form of ∫du/(u√(a2-u2) The Attempt at a Solution setting u=4x a=3 and du=4dx so 1/4du=dx I get: -5/12 sech-1(4x/3) + C Is this right or am I using the wrong definition? Just trying to...

Homework Statement The relationship between arctanh and log is: arctanh(x)=\frac{1}{2}log(\frac{1+x}{1-x}) but if i take x=1.5, I have: arctanh(1.5)=0.8047 + 1.5708i and \frac{1}{2}log(\frac{1+1.5}{1-1.5})=0.8047 + 1.5708i as expected, but using the laws of logarithm, why does this...

Hello again :) I get the feeling I'm missing some kind of 'trick', as this is proving a very difficult question :( I'll write out my frustration below; Homework Statement Find f'(x) if f(x) = \int^{cosh(x^{2})}_{0} tanh(t^2)dt Homework Equations --- The Attempt at a Solution My idea was...

Hi, first post here at PF :) I have a problem here regarding orbit propagation. Basically my situation is as follows: I have coded a system that can track the orbital parameters from an object in a simulated orbit (Basic rigidbody physics). The system takes the state vectors of the orbiting...

Homework Statement verify these identities: 1) tanh^2 x + sech^2 x =1 2) sinh(x+y) = sinh cosh y + cosh x sinh y Homework Equations cosh2x - sinh2x = 1 sech2x + tanh2x = 1 coth2x - csch2x = 1 sinh (x ± y) = sinh x cosh y ± cosh x sinh y cosh (x ± y) = cosh x cosh y ± sinh x...

Most books and websites define the hyperbolic distance element and the corresponding shortest paths in the upper half plane with no explanation. I found a derivation for them in a book called Visual Complex Analysis by Needham and it relied on mapping the "pseudosphere" onto the upper half...

Homework Statement derive the formula inverse sinhx = ln(x+sqrt(x^2+1)) for all real x Homework Equations sinhx=(e^x-e^-x)/2 ? The Attempt at a Solution i have been staring at this for awhile and i don't know how to start what should be the first step towards deriving that...

The Problem is when I Compute the Inverse I have to solutions sech^{-1}(x) = ln(\frac{1\pm \sqrt{1-x^{2}}}{x}) : 0<x\leq 1 And this not function which of them I will choose Another Question is how can I prove without the graph that csch (x) is one - to -one thanks

I get different result than stated in the book. What am I doing wrong? Homework Statement A spacecraft returning from a lunar mission approaches Earth on a hyperbolic trajectory. At its closest approach A it is at an altitude of 5000 km, traveling at 10 km/s. At A retrorockets are fired to...

Homework Statement \int\left(1+x^{2}\right)^{\frac{3}{2}}dx Homework Equations The hyperbolic functions. The Attempt at a Solution We've been going over hyperbolic substitutions in class so I assume I'm meant to use one of those, but I'm just not sure how to choose which one. Any help...

Homework Statement I'm trying to derive Equation (1) from the paper: http://idv.sinica.edu.tw/jwang/EP101/Paul-Trap/Winter%2091%20ajp%20demo%20trapping%20dust.pdf We are working with a cylindrically symmetric geometry along the z-axis. r^2 = x^2 + y^2 We have electrodes described by...

Homework Statement \int \;\sinh(2x) \cosh(2x) dx The Attempt at a Solution I let u = sinh(2x), du = 2cosh(2x)dx Integrating I shuold get\frac{1}{4} sinh^2 (2x) + C But http://www.wolframalpha.com/input/?i=Integrate[cosh%282x%29%28sinh%282x%29%29%2Cx] says I need to let u = 2x first. Why? I...

Homework Statement How could one apply differentiation formulas on this one: \partial^{2}\left(2sinh(nx)\div\sqrt{sinh(2L)-2L}\right)\div\partial x^{2} Homework Equations The Attempt at a Solution is this differentiation formula enough to differentiate:

Homework Statement The book has it exp(-MgbH/KT) =(sinh(2S+1)x/2)/(sinh(x/2)) for M=2S+1, and x = gbH/(kt). Homework Equations The Attempt at a Solution I'd have it as cosh(Mx)-sinh(Mx). How did they get the above result? Help please. Thanks.

1. \sin \theta = \cos \theta \theta=\frac{\pi}{4} 2. \sin \theta = \tan \theta \theta = 0 3. \cos \theta = \tan \theta \theta =\arcsin (\varphi -1) 4. \sin \theta = \csc \theta \theta = \frac{\pi}{2} 5. \sin \theta =\sec \theta \theta does not exist. 6. \sin \theta =\cot...

Well, I created this thread (under Geometry/Topology) about the Law of Sines, specifically for the three kinds of geometries. http://en.wikipedia.org/wiki/Law_of_sines http://mathworld.wolfram.com/LawofSines.html The Law of Sines states that, for a triangle ABC with angles A, B, C, and...

Solve the first order hyperbolic equation 3 du/dx + 2x du/dt =2u With initial condition: u(x,0) = 2x+4 My attempt at a solution I usually adopt the method of characteristics: dx/a = dt/b = du/c So from the above: a=3, b=2x and c=2u am I on the right track here?

Hello, I'm trying to calculate the following equation which is the derivative in 'x' of a distribution function: d(dxF)/dt = d(Efield.(dvxF))/dx The problem comes because the right hand of the equation is solved by using central difference, but there is a zone where there is a...

I'm reading a book on an introduction to non-Euclidean geometry, and it starts off with the usual Euclidean geometry. I didn't really need a line to be defined in that case, since it's obvious, but now that the parallel postulate has been replaced and we are working with non-Euclidean geometry...

In many cfd textbooks the domain of dependence is stated as the entire region emclosed by the characteristics. Is this correct? Isnt it only the values on the characteristics? Thanks!

Hello, I wish to find a function similar to, y^2-x^2=1 but instead of the slope of the asymptotes being +/- 1, I need one of the asymptotes to be of slope 0. That is, I wish to find a hyperbolic function with one horizontal asymptote and the other of slope 1. Is this possible?

Homework Statement Express the function cosh(6x) in terms of powers of cosh(x) Homework Equations The Attempt at a Solution Okay the problem booklet also asks me to do the opposite. Express cosh(x)^6 as mutiples of cosh(x). I can do that fine, I just simply write it out as [1/2(e^x + e^-x)]^6...

Hi, have worked out the formula for a hyperbolic spiral space curve to be r(t)=1/t X cos(alpha)+1/t X sine(alpha) + t and obtained the tangent vector T, normal vector N, and curvature (kappa) with the z axis being the central axis of the spiral. Am having trouble finding the formula for the...

So, in integrals that lead to inverse hyperbolics and can be solved with trigonometric substitution i just get lost. I know how to use both of them but i don't know which to use. For the sake of simplicity i'll just go with this one ∫ dx/sqrt(4+x^2) We know this equals arcsinh(x/2)...

Hi, My brain is not working today. So can someone please tell me what I am doing wrong. (^2 = squared) coshy^2 - sinhy^2 = 1, how do I rearrange this for coshy^2 I keep getting: coshy^2 = 1 + Sinhy^2 The book that I'm looking at has it this way: coshy^2 = Sinhy^2 + 1 Thanks Obs

Homework Statement tanh{[(2 *g*t)/(c)]+[(2*g*exp(-rt))/(r*c)]-[(2*)/(r*c)]} in terms of t Homework Equations when I plug into maple I get -(1/4)*c*ln(tanh(2*g*(t+1/r(e^(-rt))-1/r)/c)-1)/g-(1/4)*c*ln(tanh(2*g*(t+1/r(e^(-rt))-1/r)/c)+1)/g The Attempt at a Solution This cannot be...

I'm trying to understand how structures based on conic sections work. For example, when people speak of a parabolic mirror or a parabolic orbit for a satalite, I know what they mean, but when they speak of a hyperbolic mirror or a hyperbolic orbit, what does that actually mean? Is a hyperbolic...

How do you explain the structural benefits of a hyperbolic paraboloid roof? I think the 2 catenaries help distribute the weight better, but not I'm not sure if there are additional properties for this design. Thanks for your help...

I just learned about hyperbolic functions in my calculus class, and though my professor attempted to explain the use of hyperbolic functions, he really did not go very far into it, just providing a weak example ("If two people are holding a chain, cosh(x) factors into how much the chain...

I am a noob so please let me know if here isn't the right place to post this. Recently I am trying to solve hyperbolic equation m*dU/dt=k*d^2U/dx^2+q using Crank-Nicholson and finite element method. The final form of the solution is to compute the increment of the unknown at each time step...

I am trying to find the convex hull of a finite set in a hyperbolic space, particularly the Poincare disk, but the Upper Half plane works as well. I know the following equivalent definitions of the Convex Hull: 1) It is the smallest convex set containing the points 2) If the set is...

Where do the definitions of hyperbolic functions in terms of exponentials come from ?

I have a problem that deals with the inverse sech function. sech-1 x Trouble is I don't know how to define this in terms of ex Such as: How would I represent the function sech^-1 x, by definition?