Sine Definition and 511 Threads

Homework Statement If f(x) = ∫sin x0 √(1+t2)dt and g(y) = ∫3y f(x)dx, find g''(pi/6)? Homework Equations FTC: F(x) = ∫f(x)dx ∫ab f(t)dt = F(b) - F(a) Chain Rule: f(x) = g(h(x)) f'(x) = g'(h(x))h'(x)The Attempt at a Solution I tried u-substition setting u = tan(x) for the first dirivative...

Hi can someone please clarify info regarding the application and validity of the Dickey Fuller test. If I perform the test using a sine wave would I be required to somehow take into account the seasonality. From my understanding a sine wave is non stationary, using the MATLAB command below I...

Hi, I just read a physics paper and there it expands signum of a sine function as below: sgn(sin(wt))=(4/pi)*{sin(wt)+(1/3)*sin(3wt)+(1/5)*sin(5wt)+...} How can we expand sgn(sin(wt)) like this? Thanks.

Hi all, I understand the concept of group velocity when applied to superimposed sine waves of the same amplitude, and even when applied to wave packets (in which case you get the well-known expression ∂ω/∂k). My question is what happens when you add two sine waves of different amplitudes? So...

Hello, I'm trying to solve Fourier Series, but I have a question. I know that cos(nx) is even and sin(nx) is odd. But what does this mean when I take the integral or sum of cos(nx) or sin(nx)? Do they have a value or do they just keep their form?

Please excuse the usual rambling preamble (or should that be pre-ramble?), but last year, when idly searching on-line, I happened to chance upon a truly great, great paper by Shin-ya Koyama and Nobushige Kurokawa, concerning the "Multiple Sine function", $$\mathscr{S}_n(x)$$. The (free) paper in...

Hi! Many students know that A\sin(x) + B\cos(x) =\sqrt{A^2+B^2} \sin{(x+\arctan \frac{B}{A})}. I have seen just one deduction of that relation, showed by set up a system of two equations, solving for amplitude and phase shift. Is it possible to deduce the relation in a vectorial way, or in...

So using the sine law, I found that Θ = 68 degrees. And the I found that the other possibility of Θ would be 112 degrees (180 - 68 = 112). However, the textbook says that the answers are Θ = 68 and Θ = 23. What did I do wrong? Thanks.

Sorry if this sounds like a dumb question, but why is the effective value of a sine wave 0.707, as opposed to 0.637 which is the value generated by finding the definite integral over the domain [0,∏] divided length of the domain?

Please see question 9ii: Paper: http://www.edexcel.com/migrationdocuments/QP%20GCE%20Curriculum%202000/January%202012%20-%20QP/6664_01_que_20120307.pdf Mark scheme: http://www.edexcel.com/migrationdocuments/QP%20GCE%20Curriculum%202000/January%202012%20-%20MS/6664_01_msc_20120123.pdf This is my...

Hello i would like to know, how does LM324 create a sine wave after the output of the op amp?? thanks

Homework Statement Evaluate the integral. Homework Equations \int e^{2x} sin(3x) dx The Attempt at a Solution I began by using integration by parts. u = sin(3x) v = \frac {e^{2x}} {2} du = 3 cos(3x) dv = e^{2x} dx but I get stuck after that because the...

I have a range of sine waves I have obtained in an experiment. I want to put a measure on the purity of these sine waves - how well the reproduce a theoretical sine wave. Is there anyway I can analyse the FFT of the sine waves in Matlab and put a measure on the purity of the sine wave...

Hello everyone. Can someone explain the relationship between the idea of a sine wave, and the idea of a sine angle? I'm getting into trig, and I hear both terms of sin tossed around, but they seem to be completely unrelated. What does the angle of the triangle have to do with a wave? Same...

I need to add together the following sine waves and express the answer in the same form: Va = 2 sin (314.2t) + Vb = 2 sin(314.2t - 120°) Any help would be greatly appreciated.

Homework Statement I am going over a practice exam, and I need to find the FSS of f(x)=x(\pi^2-x^2) Homework Equations f(x) \sim \sum^\infty_{n=1}a_n sin\left(\frac{n \pi x}{L}\right) a_n=\frac{2}{L}\int^L_0 f(x)sin\left(\frac{n\pi x}{L}\right)dx The Attempt at a Solution I think I...

Hello all, I'm new to electrical engineering, and I'm working on a project that requires a bit more than I'm familiar with. What I'm asking for help on boils down to this: I have a circuit that outputs a low power sine wave (frequency 25-40kHz) with an amplitude +/- 5V at a few watts. I want to...

Hey I didn't understand the transition below, I'd be glad for some help thanks

Homework Statement Find the volume generated by revolving one arch of the curve y = 5 sin(x) about the x-axis. The attempt at a solution So I figured this would create a disc so I would have to use that the volume is ∏r^2 where r=sinx, r^2= (sin(x))^2 and that the way I should...

I have been trying to implement this Wave equation into java: A = amplitude of wave L = wave length w = spatial angular frequency s = speed wt = temporal angular frequency d = direction FI = initiatory phase Y（x，y，t）=A*cos（w *（x，y）+ wt*t + FI; I...

To prove that $$sin^{-1}(ix)=2n\pi\pm i log(\sqrt{1+x^2}+x)$$ I can prove $$sin^{-1}(ix)=2n\pi+ i log(\sqrt{1+x^2}+x)$$ but facing problem to prove $$sin^{-1}(ix)=2n\pi- i log(\sqrt{1+x^2}+x)$$ Help please

I'm going through my notes and I don't understand how they have included position in an equation to describe an EM wave. The equation is of the form http://upload.wikimedia.org/math/f/6/3/f6386c1751b91ec23c7123b15a11b52f.png [Asin(kx-ωt)]. This equation is just stated in my notes and there is no...

Hi, I am trying to use SR830 lock amplifier at scientific experintal. I need to apply the signal from SINE OUT BNC output in a thin ceramic sample. My sample is an plane disk with electrodes in opposite faces. This sample is isolante material, but sometimes the voltage can damage...

Consider \(u_{tt} - u_{xx} = \sin(u)\). Let \(u(\xi) = u(x - ct)\). How do we get \((1 - c^2)u_{\xi\xi} = \sin(u)\)? \[ u_{\xi\xi} = u_{xx} - c^2u_{tt} \] Correct?

pi ∫sin^2(nx)/sin^2(x) dx 0 I tried using mathematical induction and did arrive at the correct result but was wondering if a better method could be used to solve it?

This thread will be dedicated to find a general formula for the integral $$I(a,t) = \int^t_0 x \log|\sin(a x )| \, dx \,\,\,\,\, a,t>0$$ This is not a tutorial . Any comments or attempts are always be welcomed .

Homework Statement x''(t)+r*x't+kx=0 Suppose that for some initial conditions the solution is given by x=e^(-2t)*(3cos(t)+4sin(t)) What are are and k? Homework Equations See aboveThe Attempt at a Solution I've tried to "brute force" the solution simply by sticking the expression for x...

I know that normal DC can be inverted to square wave , modified sine wave or pure sine wave , what about half sine wave dc , like the one resulted from ac current passing through a simple diode rectifier, can this be inverted?

Find the Fourier SIne Series for f(x) = x on -L < x < L (Full Fourier) Ok, so my issue is in calculating the coefficients for the sine and cosine parts, more so an interpretation. So I have calulated the sine and cosine series to this point: let An: Cosine series Bn: sine series...

Homework Statement Hi guys I was wondering how to find the points of intersections between 3 different sine graphs. For an assignment I am trying to find when my three biorhythms (Physical, Emotional, Intellectual) will all cross at once. Each cycle runs on the following time frame...

Is Sine Wave just a graph of particles that do SHM? A wave on a string is also a Sine wave provided its particles are moving sinusoidally. But its shape also kind of represents a sine wave. So is the wave on a string called a sine wave because of the physical shape that we can see or because...

Hi! This is a problem regarding a quarter car model driving over a sinusoidal road excitation. A sinusoidal excitation can be written on the form ze^(jωt), z being vertical. I would like to write the longitudinal excitation of a sine wave on the same form? Any hints and tips are much appreciated.

Homework Statement A function F(x) = x(L-x) between zero and L. Use the basis of the preceding problem to write this vector in terms of its components: F(x)= \sum_{n=1}^{\infty}\alpha _{n}\vec{e_{n}} If you take the result of using this basis and write the resulting function outside the...

Sorry for the wording of the topic- I couldn't figure out how to make it fit. If I passed a hypothetical square wave through a material- be it wood, glass, cotton, etc.- would it change to look more like a sine wave?

Homework Statement lim x-> ∞ xsin(1/x) Homework Equations The Attempt at a Solution I know that this is an ∞.0 type limit but I can't figure out how to change the sin function. Thank you

How to prove that a gaussian random variable multiplied by a deterministic sinusoid also results in a random variable with gaussian pdf? Suppose here A is a guassian random variable and B is given as below where fc is the frequency of sinusoid and t is the time. B=A∗cos(2π fc t). Is random...

Homework Statement Sketch Vo for the network shown (see attachment) and determine the dc voltage available. Homework Equations The Attempt at a Solution Vi is a sine like wave with amplitude of 100 V and goes on for one period. When Vi is positive, the diode on the right goes...

Here are the questions: I have posted a link there to this topic so the OP can see my work.

Everything is in the picture I've attached. I believe my work is right because it's not that difficult of a problem but what I'm having a hard time seeing is how i go from the coefficient bn that I've calculated to the final solution. Maybe I did screw up or maybe there's an identity I'm not...

I use part of [SIZE="5"]HS-Scientist derivation in another post thanks to his detail derivation. I want to solving ## \int_0^{\pi} \sin(x sin(\theta)) d\theta## \int_0^{\pi} \sin^m(\theta) d\theta=-\frac{1}{m}\left[sin^{m-1}(x)cos(\theta)\right]_0^{\pi}+\frac{m-1}{m} \int sin^{m-2}(\theta)...

Homework Statement Any ideas for how to solve the following integral? $$\int_{0}^{\pi}\sin{n x}\sin{x}^3 dx$$ where n is a positive integer Homework Equations Various sine and cosine identities The Attempt at a Solution I haven't much of a clue how to solve the integral...

\int\frac{2x^2sin(4x)}{1 + x^6}dx The solution should be substitution method... So far I've set u = x^3 , and made some progress trying to make the integral ready to become an arctan: \frac{2}{3}\int\frac{sin(4x)}{1 + u^2}du The set up would be fine if it were not for the sine term...

I was wondering if someone could take the time to show a proof for the sum and difference identity for sine. I've seen and learned to understand some other identities, but never this one. I've been trying to understand more of the "why" than the "how" of mathematics, and this one is very...

Homework Statement Find the derivative of (sin x) ^ ((sin(sin x)))Homework Equations The Attempt at a Solution I get sin(sin x) * [(sin x) ^ {(sin(sinx)-1)}* cos x] The cos x isn't part of the exponent Is this right? Thanks :)

I am verifying the equation of radiation power of dipole antenna. I found mistakes in the derivation in the notes. I know the final equation is correct. So instead of following the steps in the notes, I reverse the step by using the final formula and going back step by step. Here is the final...

Can anyone help me with this? I've been trying to figure it out but no luck. Where do I plot the points and how do I sketch the graph? All help is greatly appreciated!

This is not really a homework, I am trying to expand Si(x) into a series.The series expansion of Si(x) is given in articles: Si(x)=\int_0^x \frac{\sin\theta}{\theta}d\theta=\sum_0^{\infty}\frac {(-1)^k x^{2k+1}}{(2k+1)(2k+1)!} This is my work, I just cannot get the right answer: Si(x)=\int_0^x...

I want to study a little bit more of Sine and Cosine Integral. I looked through all my textbooks including Calculus, ODE, PDE, Linear Algebra...Nothing! I found info on the web, but mostly are definitions. Where is this subject belongs to? Anyone can give me a link to a more complete...

Hello MHB, I got stuck on integrate this function $$\int \frac{\sin^3(\sqrt{x})}{\sqrt{x}}dx$$ my first thinking was rewrite it as $$\int \frac{\sin^2(\sqrt{x})\sin(\sqrt{x})}{\sqrt{x}}dx$$ then use the identity $$\cos^2(x)+\sin^2(x)=1 \ \therefore \sin^2x=1- \cos^2(x)$$ $$\int...

Homework Statement I'm in a Year 10 Physics class, and we have been doing an experiment about Snell's Law (θincident = θrefracted). The experimental design is fairly simple: a beam of light (from a ray box with a single slit in front of it) is shone into a glass block. The angles of the...