Hyperbolic Definition and 347 Threads

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...

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...

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...

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...

Geodesics of hyperbolic paraboloid (urgent!) Help me find the geodesics of the hyperbolic paraboloid z=xy passing through (0,0,0). I know that lines and normal sections are geodesics. Based on a picture, I think y=x and y=-x are 2 line geodesics. Then, maybe the planes in the z-y and z-x...

i am having some difficulties in proving that y=chx=(e^x+e^(-x))/2 is decreasing in the interval (- infinity,0) and increasing in (0, infinity) i know that a function is increasing in (a,b) if for two variables from that interval let's say x' and x" that are related x'<x" than...

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...

(d2^u/dt^2) - (delta u) = 0 is called a hyperbolic equation. Why is this? What makes an equation a hyperbolic equation?

Crank-Nicolson method for solving hyperbolic PDE? Hi. I'm not really sure if this is the right part of the forum to ask since it's not really a home-work "problem". Anyway, the question seemed too trivial to ask in the general math forum. What I'm wondering is wether the Crank-Nicolson...

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.

I need to determine an algebraic form for arcsech(x) = ? So far what I've come up with is as follows: \L\ \begin{array}{l} 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} -...

Hi everyone, I was in the middle of solving a physics problem and came across a math term I am having trouble solving. It is the hyperbolic sine term in this equation: T=\frac{2.0x10^{-8}}{sinh^{2}[\frac{\sqrt{130(2.6x10^{10}-130)}}{1.05x10^{-34}}6x10^{11}]+2.0x10^{-8}} When plugging...

it says to use exponentials to prove: tanh (iu) = i tan u however i do not get the correct relationship, is this an error in the question perhaps

I am not really sure if I am doing this problem correctly if you could point out any errors that would be great. The problem: The coordinates of a hyperbolic system (u,v,z) are related to a set of cartesian coordinates (x,y,z) by the equations u=x^2-y^2 v=2xy...

lets see here, I am trying to integrate this(and sorry, i don't know how to use the symbols - ill use '{' as my integral sign): 6 { 1 / (t^2 - 9) ^ .5 4 so, considering { 1 / (x^2 - 1) ^ .5 = inverse cosh(x) i did: 6 (1/3) { 1 / ((t / 3) ^ 2 - 1) ^ .5 4 then...

I'm working on a pre-freshman year math packet for college, and at one point it asks for the derivative of sinh-1(x), followed up by the derivative of ln( x + sqrt(1+x2) ). In high school, we never really covered hyperbolic trigonometry, but I have previously derived that the inverse of sinh is...

I've been reading Penrose's Road to Reality where he presents two formulas for area of shperical triangles. the first is Lamberts which is pi-(A+B+C)=area (where A,B,C are angles of triangle) the other is Harriot's which is Area=R^2(A+B+C-Pi) What I'm trying to figure out is if the...

Most structures we see in the universe are of a spherical or circular nature. However, our universe is most likely hyperbolic (saddle-shaped) overall. Is it possible that there exist material structures on the large scale that manifest hyberbolic geometry?

Speculation for helical mechanics in space-time. These illustrations may demonstrate [not prove] how Euclidean space [anthropic perspective] may coexist with hyperbolic space of Gaussian curvature and elliptic space of Riemannian curvature. [The hyperbola is reciprocal to the ellipse in...

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...

I was just reading a very cool article called "Knit Theory" in the March issue of Discover magazine. Mathematician Daina Taimina came up with the very clever idea of representing hyperbolic geometric forms as crocheted models. The idea was born out of necessity when she went to teach a class...

Hi, I have the following function to evaluate in a power series: f(a)=\frac{\pi}{8d}\frac{1}{\left (\sinh \left ( \frac{\pi a}{2 d} \right) \right)^2} Maple computes then following f(a) = \frac{\pi}{8d} \left ( \frac{4 d^2}{\pi^2 a^2} - \frac{1}{3} + O(a^2) \right) When I ask Maple if this...

Hi, I'm trying to find a way to prove that \sum_{n=1}^{\infty} n e^{-n x} = \frac{1}{4}\sinh^{-2} \frac{x}{2} Any help greatly appreciated

What is a globally hyperbolic spacetime? I'm reading birrel and davies 'quantum fields' in curved space and chapter 3 starts with this assumption... Thanks in advance.

Hey, Need help in the steps to take to find the derivative of y=cosh(x^2 + loge(x)) and e^y +ytanh(x) = x I have never seen them before, therefor not sure which rule to use, I am thinking the second needs partial derivatives :bugeye: Thanks!

I just got a clue as to why 0.5(e^x + e^-x) was called "hyperbolic cosine" and 0.5(e^x - e^-x) is called "hyperbolic sine". It is because the "complex version" reads cos(x)=\frac{e^{ix}+e^{-ix}}{2} sin(x)=\frac{e^{ix}-e^{-ix}}{2i} That explains the "cos" and "sin" part in "cosh" and...

I need to find a set of parametric equations for a hyperbolic paraboloid. The hint is that I should review some trigonometric identities that involve differences of squares that equal 1. The equation is: \frac{y^2}{2}- \frac{x^2}{4} - \frac{z^2}{9} = 1 And what I have is...

hello everyone..could you please help me with these 2: cosh^2 X=(cosh (2X)+1)/2 sinh(X+Y)=sinh X.cosh Y+cosh X.sinh Y

This isn't exactly homework but I thought it was too basic to justify putting this post in the general math section. My question is: why is arcoshx defined as: arcoshx=ln[x+rt(x^2-1)] and not +-ln[x+rt(x^2-1)] ? Is it simply to keep it as a one to one function? I know that to have an inverse a...

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...

If true hyperbolic trajectories really exist, then why has there not been any material discovered as originating from another star system?

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

When you are dealing with the Beltrami-Poincare half plane model, and you have an h-line that is horiztonal, how can you calculate the distance of two points on the horizontal line? For example, say you have the points (-9, 12) and (9,12). Then to calculate the distance you need a semicircle...

solve Uxx-3Uxt-4Utt=0 (hyperbolic) help! solve Uxx-3Uxt-4Utt=0 with u(x,0)=x^2 and Ut(x,0)=e^x I know that this is hyperbolic since D=(-1.5)^2+4 >0 so I have to transform the variables x and t linearly to obtain the wave equation of the form (Utt-c^2Uxx=0). The above equation is equivalent...

A comet is first seen at a distance of d AUs from the Sun and is traveling with a speed of q times the Earth's speed. Apparently it can be shown that if q2·d is greater than, equal to, or less than 2, then the comet's orbit will be hyperbolic, parabolic or elliptical respectively. Any idea...

Hi, if you see: cosh kx (1 + i), do you consider the (1 + i) to be multiplying the cosh or inside the cosh ? i.e. cosh kx (1 + i) = (cosh (kx))*(1 + i) or cosh kx (1 + i) = cosh ((kx)*(1 + i)) I saw this in a thermoconductivity bible from the 50's written by a really...

Could someone tell me if I'm right or wong... I want to calculate de hyperbolic excess speed for a spacecraft that leaves Earth parking orbit on a hyperbolic orbit in direction to Jupiter to arrive there in optimum conditions. It's not an Hohmann heliocentric transfer! so, i though...

This paper : Hyperbolic Universes with a Horned Topology and the CMB Anisotropy http://arxiv.org/astro-ph/0403597 ...press release: http://www.newscientist.com/news/news.jsp?id=ns99994879 proposes a universe with the shape of a horn. This is a hyperbolic space with negative...

at what point on the curve y=\cosh x does the tangent have slope 1 I have no idea how to approach this problem my work 1=\sinh x\frac{dy}{dx} \frac{1}{sinh x}=\frac{dy}{dx}

I need help proving this hyperbolic function Prove that \tan^{-1}\hbar {x}=\frac{1}{2}\ln\frac{1+x}{1-x} my work x=e^y-e^-y/e^y+e^-y (e^y+e^-y)x=e^y-e^-y 0=e^y-e^-y-xe^y+xe^-y e^y(e^y-e^-y-xe^y+xe^-y) e^2y-x(e^2y)-1+x=0 I know i have to use the quadratic equation here