Sine Definition and 511 Threads

I have included a screenshot of a part of my textbook that is giving me a slight bit of confusion. It's talking about how to get the formula for adding sines and cosines. The part that I am confused about is the very first formula introduced in the screenshot. From what I understand, we are...

How to prove this integral, $$\int_{0}^{2\pi}\sin\left({x\over 2}\right)\ln^2\left[\sin\left({x\over 4}\right)\sin\left({x\over 8}\right)\right]={27\over 2}+\ln^2(2)+\ln(2)$$

Homework Statement \int_0^{2018 \pi} \lvert \sin(2018x) \lvert \mbox{d}x Homework EquationsThe Attempt at a Solution So the period is: \frac{2 \pi}{ 2018} Each "hump" of the sine has an area of 2 so if I count the number of humps I am done. In one period of an absolute sine function the...

Homework Statement In a photoelectric effect experiment, a monochromatic plane wave of light falls on a metal plate. The electric field in the light wave at a point near the plate varies according to E=E_0 \cos (\omega t). This results in a saturation current of 6 μA. If instead, the light wave...

i was desigining a simple ( simple as in no MPPT) PV-pump standalone system, and we decided on using an AC-pump, so while i was searching for inverters i noticed the remarkable difference in price ranges, so i started to read about the difference between the two, so far the disadvantages of the...

Homework Statement The equation y = A sin(kx - wt + pi/2) is the same as a. y = -A sin(kx - wt + pi/2) b. y = A cos(kx - wt) c. y = -A cos(kx - wt) d. y = -A sin(kx - wt - pi/2) e. y = A sin(kx - wt + (3pi)/2) Homework Equations y = A sin[(2pi)/lamda * x - (2pi)/period * t + (phase constant)]...

Hello all. After completing a problem in which we derived the formulas for potential and spring force energy as functions of time, with simple harmonic motion I noticed the equations are EXACTLY the same, but with sine and cosine switched. The equations were: A sin^2(pi * t) A cos^2(pi * t) I...

Dear all Something is bugging me. I hope you can help. I read in texts that if f(t) = sin(t) then the period of the function is the time taken (secs) to complete one cycle. I also read in texts that if f(t) = sin(2t) then the period of the halved. No problems here. I see that (2*t) = (omega*t)...

Hello, I am numerically plotting a sine function sin(x) with amplitude 1 from x=0 to x=15. No problem with that. The next step gives me problems: I would like the sine function amplitude to decay exponentially starting at x=5 and not before that (the amplitude remains 1). I think I need to...

Homework Statement So in an AC circuit with inductance, I found I = (-ε_{max} cos(ωt)) / ωL I want to rewrite this as a sine function.Homework EquationsThe Attempt at a Solution I can ignore ε_{max} / ωL and work with -cos(ωt) I set ωt = θ I know cos(θ) = sin(θ+pi/2) so -cosθ =...

Homework Statement Homework Equations cos2x = (1+cos2x)/2 sin2x = (1-cos2x)/2 The Attempt at a Solution I believe you would use the double angle formula repeatedly but that is very tedious; is there a more concise way to solve the problem?

I'm new to electronics, and using my new equiptment I would like to generate a sine signal on my function generator and display it on my oscilloscope. Equipment: * The scope is Rigol DS1054Z * Function generator is a $60 digital chinese. My problem is: When I plug connect the function...

Hi, I am a neophyte in Discrete Fourier Transform and I am procticing with discrete Sine-transform. Specifically I want to calculate $$ \mathcal{F}_s \lbrace x \cdot e^{-x^2} \rbrace = \int\limits_{0}^{\infty } x \cdot e^{-x^2} \cdot \sin\left(x\right)\, \mathrm{d}x = \frac{1}{2} \pi^2 \omega...

So my question is, how does this work (hopefully I'm allowed to do hyperlinks): https://www.desmos.com/calculator/zlvrts7mul Given a table of x and y coordinates, how do I find the sin wave of best fit. I need to get f (frequency), a (amplitude), and p (phase) for the function in this form f(x)...

So I am just working with a synth and I am having it create a single sine wave. I am then looking at the output on a db vs frequency graph and I would expect the db to only be reading at the frequency of that sine wave, but there are readings from 20 Hz all the way to 2k Hz sometimes(althought...

Homework Statement Homework EquationsThe Attempt at a Solution Every small part of the trajectory can be taken as a circular arc. Then, $$\frac { m v^2} R ≤ kmg $$ But how to find out R from the sine-curve?

Homework Statement Given the wave form, determine the period, frequency, peak amplitude, peak to peak amplitude, voltage offset, phase angle, signal equation, rms voltage.Homework EquationsThe Attempt at a Solution Hi! So the main issue I'm having with this problem is reading the values I need...

Homework Statement Calculate the following limit: Homework EquationsThe Attempt at a Solution I don't know how to proceed with this. I've tried to multiply by the conjugate, and to simplify the expression (x+\pi) to u, but I wasn't very sucessful. To what kind of algebric device I could...

Homework Statement "Calculate the net force with the resultant angle acting on each object indicated in the diagram." The line going off to the southeast is supposed to be straight. My computer art skills aren't great. | 22 N | |_ _ _ _ _ \ ) 35 degrees \ \ 38 N 2...

Hello! (Wave) I want to find the Fourier series of $f(x)=x, 0 \leq x<1$. It is a series with period $1$. In our case, the function is odd. So in order to find the Fourier series, we would find the odd extension of $f$ and then use the following formulas: $a_n=0 , \ \ \forall n \geq 0$...

I have this second order differential equation but I'm stumped as to how to solve this since the zeroth order term has a Sine function in it and the variable is embedded. ##\ddot y(t) + 3H (1+Q) \dot y(t) -m^2 f \sin(\frac{y(t)}{f}) = 0## ##H~##, ##~Q~##, ##~m~##, and ##~f~## are just...

Homework Statement A rectangular box measuring a x b x c has all its walls at temperature T1 except for the one at z=c which is held at temperature T2. When the box comes to equilibrium, the temperature function T(x,y,z) satisfies ∂T/∂t =D∇2T with the time derivative on the left equal to zero...

Homework Statement Question is provided The Attempt at a Solution The required solution is provided My question is, the examiner have used sine theta in their expression for change in potential. I keep ending up with 1 - cosine theta Second question is how did they get rid of theta in the...

Homework Statement Problem: y=2-sin\dfrac{2\pi x}{3} Homework Equations Standard Equation: y = A sin(B(x - C)) + D A: amplitude is A B: period is \dfrac{2\pi}{|b|} C: phase shift is \dfrac{C}{B} D: vertical shift is D Count Formula: \dfrac{1}{4}\cdot period (What you use to choose your...

When I press these buttons on my calculator to find the third side or an angle in a triangle, what calculation is happening? What is the logic behind it all? I know it's a very basic question, but I am only in grade 10 and have not started Math yet this year.

Here is an example of a problem I am having trouble with. I need to find the i, j, k of A. I have no issues with finding the components for B, but A I just can't wrap my head around when to use cos or sin. Especially here with double projection. I know that A is : (-10 cos70 sin30, 10 cos70...

Homework Statement \int_{}^{∞} \frac{1}{n^2 - 4} dn Homework Equations I'm trying to do this a way that it isn't usually done. Normally this is done with partial fractions. I'm trying to do it by using trig substitution using sine, which requires some algebraic manipulation. For some reason...

Homework Statement Show that any sum: Asin(α) + Bcos(α) can be written as : C sin(α+ϕ) 2. Homework Equations The Attempt at a Solution i can express cos(a) as as sin(90-a), and then try to use the formula that adds sines, but it gives the form of cos*sin. [/B]

I'm (a music academic) teaching a musical acoustics course to a very mixed group (music students, science students, and neither). Today, I covered the basic concept of simple harmonic motion and how this produces a sine wave pattern of motion over time. In the extra time we had left over, I...

Homework Statement A triangle with a hypotenuse of 13.5 and height of 11.8. Find the measure of angle P. Angle p is on the same line as the 90 degree angle and I found out that it must be sine. Homework Equations sine = opposite/hypotenuse The Attempt at a Solution sin p = 11.8/13.5 sin p =...

Question (and Answer): The answer is written in thin black, inc = increasing, dec = decreasing. Am I wrong anywhere? Thanks!

$\tiny{LCC \ \ 205 \ \ \ 8.4.12 \ \ sine \ \ substitution }$ $$\displaystyle I=\int_{1/2}^{1} \frac{\sqrt{1-{x}^{2 }}}{{x}^{2 }} \ dx $$ Substitution $$\displaystyle x = \sin \left({u}\right) \ \ \ dx=\cos\left({u}\right)\ du $$ Change of variables $$\arcsin\left({1/2...

$\tiny{LCC \ \ 205 \ \ \ 8.4.7 \ \ sine \ \ substitution }$ $\displaystyle I=\int_0^{5/2} \frac{1}{\sqrt{25-x^2}}\ dx =\frac{\pi}{6} $ $$\displaystyle x=5\sin\left({u}\right) \ \ \ dx=5\cos\left({u}\right) \ \ du $$ $$\displaystyle I=\int_0^{5/2} \frac{1}{\sqrt{25-25 \sin^2...

Please guide why answers are different in following two cases and which one is correct? Case 1. sin-1 ( – 1/2 ) – sin-1 (– 1) = 7π/6 – 3π/2 = – π/3 Case 2. sin-1 ( – 1/2 ) – sin-1 (– 1) = – sin-1 ( 1/2 ) + sin-1 (1)...

the black triangle is given, and red triangle is me trying to work it out why is my trangle wrong? and what is the right triangle? someone is sliding down a slope, with 2ms-2 of acceleration (not actually given which direction, maybe I'm wrong there, but the person is acelerating at 2ms-2 down...

Homework Statement Calculate ##\lim_{x\to 1} \frac{1}{x-1} \int_{1}^{f(x)} sin(\pi t^2) dt##. f is differentiable in the neighbourhood of point ##x=1## and ##f(1)=1##. Homework Equations If ##f## is continuous on a closed interval ##[a,b]##, then there exists ##ξ∈]a,b[## such that...

Hello, I need to find out how to generate a standing sine wave, or a quarter sine wave. I had no trouble finding out how to create a full or half wave rectifier, but very little generating a quarter wave, & that info mostly dealt with sound waves. I am doing this for experimental purposes...

Homework Statement f(x) = x , 0 <x<1/2 1/2 , 1/2 < x <1 in this question , I am not convinced that a_ 0 = 0 for half range sine series , because i found that but , thoerically , for half rang sine series , a_ 0 must be = 0 , ,am i right ? why the value of A- 0 that i got is not = 0 ...

Can you use any trigonometric wave to describe a phenomenon between two different objects? In the sense like a line or parabola would talk about a relation between two variable thanks so much in advance

Homework Statement A sinusoidal transverse wave traveling on a string is described at t=2.0s by y(x)=0.1sin(4πx+(33π/40) and at x=1.0m by y(t)=0.1sin((17π/4)+4πt) a. What is the wavelength and the amplitude? b. What is the frequency (Hz) and direction of propagation? c. What is the speed? d...

Hi! I want to define a sine function that is discontinuous at multiples of $\pi$. The multiplier is to be an integer. How can I do that? I am thinking about something like this: $$f(x)=\begin{cases}sin(x) & x \in \Bbb{R} \\ \text{undefined} & x=n \cdot \pi | n \in \Bbb{Z} \text{ and } x \in...

Homework Statement A sine function is given.And the question is At which time does the deflection (y) reaches a maximum? y= 3sin (800πxt+π/3) Homework Equations y= A sin (wt+Φ) A=amplitude w= angular frequency Φ= initial phase 3. The Attempt at a Solution I already have solution. But I don't...

< Mentor Note -- thread moved to HH from the technical physics forums, so no HH Template is shown >[/color] Say one has the equation of 90= Sin^-1(a) + Sin^-1(b), how would one made the term "b" the subject of such an equation? Please excuse any naivety.

Homework Statement A string of length L =8 is fixed at both ends. It is given a small triangular displacement and released from rest at t=0. Find out Fourier coefficient Bn. Homework Equations what should i use for U0(x) ? The Attempt at a Solution

Homework Statement For an upcoming lab I've been asked to build a circuit to convert a square wave (vi(t))e into a sine wave (v0(t)) by selecting appropriate resistor/capacitor values for the circuit below (from what I know, it's impossible to produce an accurate sine wave with just this, I...

Properly speaking, since sin(x) and cos(x) don't go to zero as x \rightarrow \infty, the following integrals are undefined: \int_0^{\infty} cos(kx) dk \int_0^{\infty} sin(kx) dk However, in the handwavy way of physicists, we can often pretend that the cosine integral "converges" to \delta(x)...

Homework Statement Find the Fourier series for the following function (0 ≤ x ≤ L): y(x) = Ax(L-x) Homework EquationsThe Attempt at a Solution 1. We start with the sum from n to infinity of A_n*sin(n*pi*x/L) where An = B_n*Ax(l-x) 2. We have the integral from 0 to L of f(x)*sin(m*pi*x/L) dx...

can someone explain how you go from (4.25) to (4.26) using Euler's formulas in the attachment?

How to find the average value of sin2wt? Mod note: Thread locked due to lack of homework template and no effort shown.

$\displaystyle \lim_{x \to 0} \frac{x^2-\sin^2{x}}{\tan(3x^4)}$ How do you calculate this one? L'hopital gives me $\displaystyle \lim_{x \to 0} \frac{2x\cos^2(3x^4)-\sin{2x}\cos^2(3x^4)}{12x^3}$