identities Definition and 416 Threads

Homework Statement \displaystyle \frac{d}{dt} (\vec u (t) \vec v (t))= \vec u (t)' \vec v(t)+\vec u(t) \vec v(t)' I know this is a product rule on the RHS but how does one prove it? Thanks

Does anyone know how to derive the Ward-Takahashi identity for a field starting from a known conserved Noether current (or equally helpful, from a known symmetry transformation of the Lagrangian)? It'll probably be enough to allow me to do it for myself if you could explain quantitatively what...

Homework Statement Sin(2α)=-8/17 Using either double angle or half angle identities, sin,cos,tan,csc,sec and cot of alpha. Homework Equations The Attempt at a Solution I tried and tried BUT i am lost because in order to find cos of alpha using identies, you still have to have...

so we have the identity \nabla\times\nabla\phi = 0 and from Maxwell's equations we have \nabla\times \textbf{E} = -\frac{d\textbf{B}}{dt} But we also have that \textbf{E} = -\nabla\phi So the problem I'm having is this -\textbf{E} = \nabla\phi which i substitute into the...

How do you do stuff like sin(pi/4) in your head or sin(1) or sec(pi(x))? Thanks for your help. I'm in Calc II and fully understand the calculus but my trig foundation from high school isn't the best.

I am currently taking Calc II and we are doing trig substitutions at the moment. I seem to have forgotten almost all the important trig identities. I understand that this sounds like something I should google but I honestly cannot find a good list of the trig identities I should know at this...

Hi, I ran this by my friend awhile ago and I'm not sure how to feel about it still... Consider the following: We know \nabla_\alpha G^{\alpha\beta}=0\implies \partial_\alpha G^{\alpha\beta}+\Gamma^{\beta}_{\gamma\delta}G^{ \gamma \delta}+\Gamma^{\delta}_{\delta\gamma}G^{ \gamma...

Homework Statement Show that arcsin(1/sqrt(5)) + arcsine(2/sqrt(5)) = Pi/2 Homework Equations The Attempt at a Solution Can someone please give me so much as a hint?

Hi, Does anyone know of any nice identities for the inverse or arc tangent of a sum or a product? Thanks, rhz

Homework Statement prove that sin^4theta + cos^4 theta =1/4 (3+cos4theta).hence,find the greatest and least value of sin^4theta + cos^4 theta. please give hints to start . no idea at all...i start from the RHS and get 2cos^4 theta - 2 cos^2 theta +1 , then how sin^4theta + cos^4 theta...

Homework Statement \int\frac{sec^{2}x}{tan^{4}x}dxHomework Equations The Attempt at a Solution I have the answer as -1/3 cot^3(x) + C listed. All the intermediate steps are given, but the first one is they have converted the sec/tan integral in to: \int{cot^{2}x}{csc^{2}x} dx I am a little...

Homework Statement tan^2x - sin^2x = sin^2x*tan^2x Homework Equations The Attempt at a Solution This is how my teacher solved it. Sin^2x sin^2x ______ - ______ Cos^2x 1 sin^2x - cos^2x*sin^2x _________________________ cos^2x = sin^2x (1-cos^2x)...

Homework Statement Prove this identity m) Sin^2 x / sin^2 x + cos x^2 = tan^2 x / 1 + tan^ x Homework Equations http://i52.tinypic.com/105tdtk.jpg Letter (m) on the top The Attempt at a Solution I don't know to much about trig identities, he barely taught anything. But...

Hello! I was wondering if they're any identities between exponential and logarithmic functions? Maybe identities isn't the right word, but what I'm talking about is something like euler's formula. Other than than {e^x} and {ln(x)} are inverses, if that counts. Any help is very much appreciative!

Homework Statement I am having issues with these. Does anyone know of a tutorial for these, like something I can print out that has sample problems with solutions on how to solve them? Thanks very much! (example problem question) (sinx + cosx)^2 = sin 2x + 1 I am just having a...

Having Trouble: Solving a Trigonometric Equation using Identities ? Homework Statement I am having problems with these. Need some help please! Here is a sample question I am having troubles with: 3 cos θ + 3 = 2 sin^2 θ, 0 <= θ < 2pi I am really struggling with these. Any help...

Homework Statement For tan(theta) = /2/3 (theta in quadrant 2) find sin(pheta) and cos(pheta) using the pythagorean identities. Homework Equations The Attempt at a Solution Which 2 pythagorean identities would I use? My trouble is with finding sin and cos from tan.

I can show that Coulomb's Law + superposition implies \nabla \cdot \mathcal {E} = \frac{\rho}{\epsilon_0} and \nabla \times \mathcal{E} = \mathbf{0}. I want to go the other way and derive Coulomb's law and superposition from the vector identities. I know that Gauss' Law implies Coulomb's law if...

Homework Statement t = tetha FInd sin 2t when cos t = 4/5 Homework Equations no idea The Attempt at a Solution no. . . . btw what should I do 1st? I don't understand this question

I was wondering if there could be more identities than i have read. I was doing questions on log and found many questions in this form:- (loga b)2 (loga b)(loga c) This is not my homework but i require these identities to solve the questions. Please someone tell me how to solve these...

Homework Statement Prove \nabla \bullet (\textbf{A} \times \textbf{B}) = \textbf{B} \bullet (\nabla \times \textbf{A}) - \textbf{A} \bullet (\nabla \times \textbf{B}) I'd like to prove this using the levi-civitia symbol: \epsilon_{ijk} and einstein-summation convention as practice and...

My book was proving that.. sin(-x) = -sin(x) tan(-x) = -tan(x) cos(-x) = cos(x) .. I posted an attachment of the books explanation.. I just don't understand how their explanation has anything to do with sin of a negative angle equaling sin of an angle times negative one, the same goes for...

Hello, I would like to ask a question on curl. The wikipedia page http://en.wikipedia.org/wiki/Vector_calculus_identities" gives formulas of various operations, among which: \nabla \times (A \times B) = A(\nabla \cdot B) - B(\nabla \cdot A) + (\underbrace {B \cdot \nabla...

Homework Statement i have to prove that ∇x(FxG)=(G⋅∇)F-(F⋅∇)G+F(∇⋅G)-G(∇⋅F) where F and G are vector fields with F=F1,F2,F3 and G=G1,G2,G3 ∇=d/dx,d/dy/d/dz Homework Equations The Attempt at a Solution i have tried applying scalar multiplication and the cross product to...

Hey, Can anyone help me solve this equation please? Thanks Homework Statement cos(3θ)=cos3θ-3sin2θcosθ Homework Equations cos(u+v) = cosu cosv - sinu sinv sin2u = 2sinu cosu The Attempt at a Solution

Hi, I've been trying for 3 hours to solve this proof using identities. I can't seem to get it. Can i get a little help please? Prove: A U B = (A ∩ B') U (A' ∩ B) U (A ∩ B) thanks

Homework Statement ArcTan(-1) = theta I figured that theta was both 7pi/4 and 3pi/4.. but the book has -pi/4 Because my two answers are both equivalent to -pi/4 would I be wrong? Homework Equations The Attempt at a Solution

Homework Statement what is the identity of a3 + b3 + c3 i am getting a bit confused please help! Homework Equations The Attempt at a Solution

Homework Statement prove that: (1+tanx)^2-2tanx=1/(1-sinx)(1+sinx)Homework Equations Main question is does 1/cosx^2 = secx^2? More in my attempt at the solution.The Attempt at a Solution (1+tanx)^2-2tanx=1/(1-sinx)(1+sinx) (1+tanx)(1+tanx)= 1+2tanx+tanx^2 1+2tanx+tanx^2-2tanx=1+tanx^2...

How would I go about showing: \hat{A}^{\dagger} + \hat{B}^{\dagger} = \left( \hat{A} + \hat{B} \right) ^{\dagger}

Homework Statement x=2acos(theta- pi/3)cos(theta) y=2acos(theta- pi/3)sin(theta) Write everything in terms of x and y Homework Equations cos(a-b)=cos(a)cos(b)+sin(a)sin(b) sina/cosa=tana etc... The Attempt at a Solution I've tried a lot of rearranging, can't figure it out.

Tan theta=sin theta/cos theta What does that identity mean? What does it say about the triangle? And what on Earth is an identity? I understand everything taught in the course so far, trig ratios, reciprocal trig ratios, special angles etc etc...but i have no idea what identities mean, some...

I'm on mobile so I can't use regular symbols. Sin80°csc80° = 1 why does this equal one? Is there multiplication involved here? I know csc = 1/sin

I'm manipulating an equation, and I think I am correct in doing this, but not sure. Could someone tell me if the equality I've written below is true? [\nabla\cdot [\rho\vec{v}\vec{v}] ]\cdot\vec{v} = \nabla\cdot[\frac{1}{2}\rho v^2 \vec{v}] (where \rho is dependent on position) *NOTE* that...

Homework Statement Can some one please give me the proof or somewhere I can find the proof or just an explanation why Sin(-theta) = -Sin(theta Cos(-theta) = cos(theta) Tan(-theta)= -Tan(theta) Thank you.. Homework Equations The Attempt at a Solution

Homework Statement prove that, (cos(3x) - cos (7x)) / (sin(7x) + sin(3x)) = tan(2x) prove that, cos(3x) = 4cos^3(x) - 3cos(x) Homework Equations tan(x) = sin(x)/cos(x) must come into the first one The Attempt at a Solution tried seperating the fraction so there is only one...

Homework Statement sin(75^\circ) Homework Equations sin(\frac{\alpha}{2}) = \pm \sqrt{\frac{1-cos(\alpha)}{2}} The answer is known to be: \frac{\sqrt{6} + \sqrt{2}}{4} The Attempt at a Solution sin(\frac{150^\circ}{2}) = \pm \sqrt{\frac{1-cos(150^\circ)}{2}} sin(\frac{150^\circ}{2}) = \pm...

Homework Statement Problem 6. If you know that tan(theta) = -4/5 and sin(theta) > 0, find: (a) sin(theta) (b) cos(theta) (c) tan(theta + pi)Homework Equations cos^2(t)+sin^2(t)=1 tan(t)=sin(t)/cos(t) The Attempt at a Solution My teacher went over this today, but likes to skip over steps that I...

When formally proving trig identities using algebra are you allowed to divide? Ordinarily I wouldn't think twice about this. Sure, the trig function by which you are dividing might take on 0, but not for all angles. We divide by potential zeros all the time. My advisor was being very coy...

Homework Statement I have been practicing proving trig. ident. for the past couple of days... although I am getting better... I wanted to ask are there any strategies that I should be aware of to make the process easier ? Homework Equations The Attempt at a Solution

I am doing this question on page 75 here (http://www.maths.cam.ac.uk/undergrad/pastpapers/2006/Part_2/list_II.pdf ). Here is my solution so far: \nabla_a\nabla_b\phi=\partial_a\partial_b\phi=\partial_b\partial_a\phi=\nabla_b\nabla_a\phi Then for the energy-momentum tensor I just wrote...

Homework Statement Prove using the Levi-Civita Tensor/Kroenecker Delta that: (AxB)x(CxD) = (A.BxD).C-(A.BxC).D Homework Equations εіјkεimn = δjmδkn – δjnδkm (where δij = +1 when i = j and 0 when i ≠ j) The Attempt at a Solution if E = (AxB) then Ei = εіјkAjBk, and if F =...

1. Homework Statement Sorry for the long intro: An object is propelled up at angle theta 45 deg. < theta < 90 deg. to the horiz. with initial vel. of V0 m/s. from the base of a plane that makes an angle of 45 deg. with the horiz. If air resistance is ingored, the distance, R, traveled by...

Proving trig identities I have 2 more this time, thanks for the time! Homework Statement -sin^2x-sin^2y+1=cos(x+y)cos(x-y) Homework Equations Compound, double, pythagorean, reciprocal, quaotient, etc. The Attempt at a Solution R.H.S. cos(x+y)cos(x-y) =...

I have been having lots of trouble verifying trigonometric identities. I know the fundamental identities but I am actually having trouble with the algebra that goes along with the problems. The problem I am working on now is: cos(x)-tan(x)/sin(x)cos(x) = csc^2 (x) - sec^2 (x) (The csc...

Homework Statement Given that cos C = 12/13 where C is a reflex and sin D = 3/5 where D is acute, find the exact value of cos ( C + D ). Homework Equations The Attempt at a Solution I used the Addition Formulae: cos(A+B) = cosAcosB-sinAsinB cos(12/13)cos(2/5) -...

Homework Statement I got this expression while solving a problem. (y+1)/(y-1)=sin2x/sin2a we need to find the range of y Homework Equations The Attempt at a Solution here y=(sin2x+sin2a)/(sin2x-sin2a) Numerator of RHS lies between sin2a-1 and 1+sin2a Denominator lies...

Homework Statement Prove cosh(2x)= cosh^2(x) + sinh^2(x) Homework Equations sinh(x) ≡ [ e^(x) - e^(-x) ] / 2 cosh(x) ≡ [ e^(x) + e^(-x) ] / 2 The Attempt at a Solution = { [ e^(x) + e^(-x) ] / 2 }² + { [ e^(x) - e^(-x) ] / 2 }² = [ e^(x) + e^(-x) ]² / 2² + [...

Homework Statement (Sin 2θ / sinθ) - (cos 2θ/ cos θ) = Sec θ just trying to match one side to the other Homework Equations all trig identities The Attempt at a Solution broke down sin2θ into 2sinθ cosθ then reduced the sinθ in the denominator giving me sinθ cosθ -...

Homework Statement integrate: sin (2x)/(1+sinx) Homework Equations (sin x)^2 + (cos x) ^2 = 1 sin (2x) = 2 sin x cos x cos (2x) = (cos x)^2 - (sin x)^2 The Attempt at a Solution I've been trying to integrate this thing for about an hour by rearranging various trig...