Sine Definition and 511 Threads

Orthogonal Properties for Sine Don't Hold if Pi is involded?? Normally I know \int_{-L}^L \sin \frac{n x}{L} \sin \frac{\m x}{L} ~ dx = 0\mbox{ if }n\not =m , \ =L \mbox{ if }n=m but apparently this doesn't work for \int_{-L}^L \sin \frac{\pi n x}{L} \sin \frac{\pi m x}{L} ~ dx I am...

Cant oscillate sine wave from "bubba" oscillator hey i can't oscillate sine wave from "bubba" oscillator using pSpice. see the following attachment. can u please help me?

HOw do you integrate sin(x)^10?

Homework Statement The problem is simply to find the image of the upper half-plane under the inverse sine function. Homework Equations The textbook defines the inverse sine in the following way. First, it defines arccos(w) = -i * log(w +/- sqrt(w^2 - 1)) and then it defines arcsin(w) = pi/2...

If two sine waves have the same frequency and amplitude but have different phase shift do they still produce a standing wave? Thanks for the help.

I'm trying to do something very simple... I'd like to have a sine function, where the frequency is controlled by a separate frequency function Something like this: g(t) = sin(2*pi*f(t)*t) Assume that f(t) = 20*exp(-2*t)+4 I would expect a sine wave that starts at 24 Hz and then...

Hi. I'm doing a lab where we hooked up an RF signal generator at 1.25MHz/10dBm to a spectrum analyzer using a 50 ohm wire. Can anyone explain to me or link me to a place where I can read about why a real sine wave's frequency spectrum is not a pulse? Also, why would with a sweep from 1 Mhz...

Homework Statement A sine wave in + x direction with max amplitude of 1 wavelength= 2.85 m wavenumber, k = 6.28/2.85 m = 2.2 rad/m w=8rad/m frequency=1.27 cyc/sec vel.= 3.63 m/sec at x = 20m t= 5.5 sec at x + 2 wavelengths x= 25.7m t=7.07 sec by definition the y displacement is the...

As a circuit element I need a 60 Hz sinewave with low harmonic distortion (maybe 1-2% max.) and precision amplitude (1-2% max) of about 2.5 volts. It should be syncronous with an input reference frequency. The reference is about 30KHz and is some as-yet-undetermined multiple of 60 Hz.

1. The sine function is given by the infinite series sin(x) = x - x3/3! + x5/5! + x7/7! + ... a) What are the forward and backward errors if we approximate the sine function by using only the first term in the series, for x = 0.1, 0.5, 1.0? b) Using the first two terms. Homework Equations...

Homework Statement prove lim h-->0 sin(h)/h = 1 Homework Equations I understand the idea of squeze theorom. Understand that area of small triangle < sector area< big triangle. I know 1/2sin(h) < 1/2h < 1/2(sin(h)/cos(h)). In my calc book it goes from sinh< h< (sinh/cosh) to...

Homework Statement We are supposed to prove that sin(x+y) = cos(x)sin(y) + sin(x)cos(y) Homework Equations cos(A-pi/2) - sin(A) sin(pi/2 - A) = Cos(A) sin(A-pi/2) = -cos(A) The Attempt at a Solution We had to prove all of the relevant equations but were allowed to work in groups...

Homework Statement Using the inequality |\sin(x)| < |x| for 0 < |x| < \frac{\pi}{2}, prove that the sine function is continuous at 0. Homework Equations Definition of continuity: A function f: R -> R is continuous at a point x0 \in R, if for any \epsilon > 0, there esists a...

Homework Statement http://s3.amazonaws.com/answer-board-image/ad36bcba0e2d0b49d556f054de19d124.jpg Variable y(t) is the position of the block of mass m, and u(t) is the position of the plate on the right. The spring is unstretched when y = u. We can think of u(t) as the input and y(t) as...

I'm trying to calculate the RMS for square, triangle and sine waves. I can easily do the integrtion for sine waves and for square waves by looking at the graphic and getting the areas. It doesn't seem as easy for triangle waves since its squared form looks much more complicated and I'm not...

Homework Statement I'm looking to determine the Fourier sine transfom of 1. Homework Equations One this site http://mechse.illinois.edu/research/dstn/teaching_files2/fouriertransforms.pdf (page 2) it gives the sine transform as \frac{2}{\pi \omega} The Attempt at a Solution...

I would like to design a Pure Sine wave inverter for DC to AC rectification. I want to drive motors with this applicaiton. (At most 120VAC .5HP) I don't want to specify too much, because the main point here is design basics. With the right information, I should be able to design accordingly. I...

Homework Statement Construct or "work backwards" from a sine graph to a sine formula. The formula should be in: y = A sin(Bx+C) +D Where A is amplitude, D is Vertical Shift (on y access) and Bx+C are arguments of the function The graph shows that the Phase Shift is 1 and Period is...

Homework Statement f(t) = \left\{ \begin{array}{rcl} 5sin(t) & \mbox{for} & 0 < t < 2\pi \\ 0 & \mbox{for} & t > 2\pi \end{array}\right. Now, the problem is about rewriting f(t). My friend and I decided that it had to be \dfrac{10 - 5e^{-2\pi s}}{s^2 + 1} However, the answer turned out...

I was finally able to figure out how to find the sine series for cos(x), but only for [0,2pi]. A question i have though is what is the interval of validity? is it only [0,pi]? Ie if I actually had to sketch the graph of the sum of the series, on all of R, would I have cosine or just a periodic...

Homework Statement Si(x)=\int(sint/t)dt from 0 to x integrand is 1 at t=0 express the solutiony(x) of the initial value problem x^3y'+2x^2y=10sinx, y(0)=0 in terms of Si(x) Homework Equations The Attempt at a Solution y'+2/xy=10x^-3sinx multiply by x^2 x^2y'+2xy=10x^-2sinx...

Homework Statement How can I prove this theorem in the triangle ABC? sin(A)/a=sin(B)/b=sin(C)/c Homework Equations A*B and ... The Attempt at a Solution I have drawn a triangle and tried to prove it, but i couldn't. (I don't know how to send a picture to my post!) I know...

Homework Statement 4 \ sin \ \theta \ = \ 3 \ csc\ \theta The Attempt at a Solution sin\ \theta \ = \ \frac {3}{4} \ csc \ \theta sin^2 \ \theta \ = \ \frac {3}{4} sin \ \theta \ = \ \pm \ \frac {\sqrt{3}}{2} 30 \ \deg \ in \ QI, \ 150 \ \deg \ in \ QII, \ 210 \ \deg \ in \...

Why are light waves/X-rays/gamma rays/etc. in the form of sine waves, rather than, say, a zig zag wave, or even a straight line? I recently watched this youtube video explaining how to visualize ten dimensions: http://www.youtube.com/watch?v=JkxieS-6WuA&feature=related And wondered if photons...

Homework Statement what is the integration of 1/2 sin y dy from 0 to pie/2 Homework Equations i know sin y = -cos y (integration) The Attempt at a Solution from 1/2 sin y dy to (1/2) -cos y then i plot pie/2 and 0 i got (1/2) [-cos (pie/2) - (-cos 0)] = 0, but the answer is 1/2...

Use the cosine and sine rules to determine the magnitude and direction of the resultant of a force of 11 kN acting at an angle of 50 degrees to the horizontal and a force of 6 kN acting at an angle of -30 degrees to the horizontal. helppp please

Could anyone tell me how to use the cross product to prove the sine rule

Homework Statement Suppose U follows a uniform distribution on the interval (0, 2pi). Find the density of sin(U) Homework Equations The Attempt at a Solution Well if U ~ (0, 2pi), then sin(U) should follow a distribution on [-1, 1]. I know one way to do tackle such problems is to...

Homework Statement If f(x) = sin²(3-x), then f ' (0) = ____ . A. -2cos3 B. -2sin3cos3 C. 6cos3 D. 2sin3cos3 E. 6sin3cos3 Homework Equations Derivative of Sinx= cosx. The Attempt at a Solution I cannot seem to figure out what the derivative would be with this...

Homework Statement For example: the function is A0sin(w0*t - B*z) If I take the partial derivative with respect to z, how do you go about this? In my years at uni, I don't know if this has ever come up. Homework Equations The Attempt at a Solution My initial thoughts are...

Homework Statement I need to calculate the angle of inclination of an air track. The hypotenuse is 229.8 +/- 0.05 cm and the opposite side (the height that one side of the track is raised to) is 1.3 +/- 0.05 cm. I need to calculate the error in the angle of inclination. Homework Equations...

Homework Statement I am doing a proof about limits, and I need to know the range that sin(n^3-2n)/n is within for all n. Homework Equations The Attempt at a Solution I know that sin(n) is in between -1 and 1 for all n, so sin(n)/n would be in between -1/n and 1/n for all n...

Hi, I was playing around with Euler's Identity, and I found something (or at least I think I found something) interesting: It is a well known identity sin(z) = [exp(iz) - exp(-iz)]/(2*i), where z is any complex number, exp is the complex exponential function, and i is the imaginary...

Homework Statement How do i find the phase between sine waves knowing the time difference between each? http://users.bigpond.net.au/exidez/sinewave.jpg Equation for the main function is 3cos(30t - Pi/2) The smaller sine wave is of the same frequency when is settles in a steady state...

Homework Statement Expand the function f(x) = x3 in a Fourier sine series on the interval 0 <= x <= 1 Homework Equations \[f\left( x \right)=\sum\limits_{k=1}^{\infty }{{{b}_{k}}\sin \left( k\pi x/a \right)}0<x\le a\] and \[{{b}_{k}}=\frac{2}{a}\int_{0}^{a}{f\left( x \right)\sin...

Help! I need to build an in-phase sine wave generator with quadrature output and its frequencies are between 1KHz-12 KHz and it need to be voltage controlled Thanks for any help anyone can provide.

I have a signal that is a sine wave plus an offset. I would like to measure the dc component and possibly also subtract it from the signal later. The signal is very slow (10th of Herz) and the offset changes on the order of minutes. I thought it should be possible to get a time average with an...

Hi everyone. I'm doing a microcontroller project where I'm using a 256 element array of 1 byte values to output a sine wave at varying frequencies. I'm using the top 8 bytes of a 16 bit "angle increment" value that's incremented by varying amounts as an index to the array of values, to control...

Hello All, I have been doing a few basic experiments with coils lately and I am trying to figure out the simplest way to drive a coil at its natural resonant frequency so that I can get the Q as high as possible. My only problem is that I don't have a sine wave generator that I can use. I...

hi all, pretty sure this is the wrong place to post this but it is a quick one so... is a sine wave always transverse? thanks

How are Square and Triangle waveforms produced from Sinusoidal waveforms? Thanks Greg

Newton's second law is taking my mind for a spin and for some reason had me contemplating how it works for several hours. This is all with respect to an incline and an object sitting on the incline with no friction. If the problem does not give you the mass of the object can you completely...

This is obviously an electronics question. In communication systems, to calculate the power of a sine wave, the formula below is used Power (Sine Wave) = 1/2 * (peak amplitude)^2 This formula is apparently a standard electronics formula. I'm trying to understand where it comes from. How...

Hi, would anyone be able to explain how to evaluate a function using orthogonality (i.e. using orthogonality to solve a definite integration problem with sines/cosines)? Thank you

Hello everyone. I am working on a present for a girl (hehe) which will play a wav sound from an SD card into headphones. So, I have an SD card connected via SPI to a microcontroller which then connects via SPI to a DAC. Right now I connected my DAC and now I am having problems outputting a...

sorry about the mistake in my last post. I miswrote the bottom vertex of the equilateral triangle. Let me re-state the problem correctly This is the 3rd and final question I post from the book, The Unsolvable and the Solvable. It is NOT a homework question. This is something for...

I am to contrast the difference between modified square wave, and synthesized sine wave inverter outputs. Am I to understand, that a modified square wave output is like a square wave, but the transtion to current flow in the other direction is delayed some at the zero point. This is to give...

This is the 3rd problem from the book, The Unsolvable and the Solvable. This is the last one I post from this book. It is pretty challenging. Once again, it is NOT a homework problem. Consider an isoceles triangle ABC and an equilateral triangle BCD which share the side BC as shown...

Here's the question: The leaning Tower of Pisa leans toward the south at an angle of 5.5°. On one day, its shadow was 90m long, and the angle of elevation from the tip of the shadow to the top of the tower is 32°. Determine the slant height of the tower. How high is the tip of the tower...

Hello. I know the definition of sine and cosine, but how were these formulas originally invented? I mean, how did people derive the power series for sine and cosine for the first time?