Sin Definition and 442 Threads

Homework Statement For the following series ∑∞an determine if they are convergent or divergent. If convergent find the sum. (ii) ∑∞n=0 cos(θ)2n+sin(θ)2n[/B]Homework Equations geometric series, [/B]The Attempt at a Solution First I have to show that the equation is convergent. Both cos(θ)...

I'm asked to transform y(t) = x(t)*x(t) (where * is the convolution product) and x(t)= sinc(t)cos(2π10t) ( sinc(t)= sin(πt)/(πt) ).The attempt at a solution Clearly everything is simple if you know X(f), because y(t)=InverseFourier{ X(f)2 }. The problem is that I can't find X(f). By the way...

Hi, I'm new to the forum as I'm struggling to find answers with an internet search. I've seen Snell's Law stated as n sin theta = constant. How does this arise from its more familiar form of n1sintheta1 = n2sintheta2? I can't work it out. Thanks for reading!

Homework Statement Prove that: ##sin x + sin 2x + cos x + cos 2x = 2\sqrt{2} cos (\frac{x}{2}) sin(\frac{3x}{2}+\frac{\pi}{4})## Homework Equations We know all the double, compound, and half angle formulas. The Attempt at a Solution Taking on the RHS, we have Expanding with half angle...

Dose anybody knw that why we take cos with dot product and Sin with cross product?

Hi, i was just wondering since cosx=1-(x^2/2) is there a similar formatted formula for sinx?? much appreciated :) :)

Determine the values of sin v, cos v, and tan v at each point P(x, y) on the terminal arm of an angle v in standard position. (b) (3, 4) ( (d) (12, 5) (f) (7, 24) for b I was able to do tan \theta= y/x tan \theta= 4/3 \theta = 53.13 My textbook says I am wrong... doing an online...

Homework Statement The given two-parameter family is a solution of the indicated differential equation on the interval (−infinity, infinity). Determine whether a member of the family can be found that satisfies the boundary conditions. (If yes, enter the solution. If an answer does not exist...

I've learned that the horizontal component is F cos angle not F sin angle, but I'm looking right now into the aqa physics a student book from nelson thrones, chapter 2.3 page 27, and it says that the horizontal components going to be made up of sin and the vertical out of cos... This is about...

Hi, I just started the chapter work and kinetic energy in my physics book, and I'm uncertain about the meaning of two symbols. They are 'F sub "two vertical lines"' and 'F sub "an upside down T/perpendicular symbol"'? Does it mean cos∠ and sin∠, respectively? Nevermind, I figured it out...

Hi! While computer programming Us encountered problem of exact calculus of trigonometry funcs. As is well known, all calculators and comp progs do x for Sin and x^2/2 for Cos on 0..Pi/2 and so on. It seems insufficient. While solving - next problem: trigon func definition without triangle.

Solving for Sin with no calculator + additional questions Sinθ=opp/hyp Sinθ=5/3 Sinθ=1.6 I know the answer is 35.87°. I would like to convert 1.6 to 35.87° but am unsure how.

Our integral \int\limits_0^{\pi/2} \sin^{2a+1}(x)\,dx Has a Factorial Form: {(2^a a!)}^2 \over (2a+1)! What is the process behind going from that integral to that factorial form? My approach which is not very insightful: I used mathematica to calculate the integral to return...

Teacher assigned this on first day due tomorrow and i have no clue on some like this one: Sin 0=Ry/Rx a.) solve for Ry b.) solve for Rx c.) solve for 0 ?

Homework Statement solve sin x - 2x = 0 The Attempt at a Solution I can see that zero is a solution, but i don't know how to actually solve it in a general way. Can somebody give me a hint?

I did this question using two different trig identities, each of which gave me a different answer when I graphed them on Wolfram Alpha. 1. First identity: sinx = 2sin(0.5x)cos(0.5x) isolating for sin(0.5x): sin(0.5x) = (sinx) / (2cos(0.5x)) The question wants sin (0.5 arcsinx): Applying...

Find the equation of a sine function with its first positive maximum point at (pi/5,8) and its next minimum point at (7pi/10,-2). With the sin form as y=a*sin[b*(x-c)] + d I found: a=[max-min]/2 = 5 b= 2pi/period= 2pi/(2*[max-min])=2 d=max+min/2=3 I am having troubles determining...

Homework Statement Write ##sin(ax)## for ##a \in \mathbb{R}##. (Use generating function for appropriate ##z##) Homework Equations ##e^{2xz-z^2}=\sum _{n=0}^{\infty }\frac{H_n(x)}{n!}z^n## The Attempt at a Solution No idea what to do. My idea was that since...

Not a direct problem but this is a homework related question so I'm posting it here. When getting components with respect to gravity it is often intuitive, this isn't always the case. None of my classes thus far have talked about why when to use sin or cos, they just do. I'm wondering how I can...

I know the Double Angle for Sine is: $$\sin(2x) = 2\sin(x) \cos(x)$$ but from the triangle given, how do I figure it out? We did this in class, but the teacher just told a small amount of things, and then let us talk amongst each other to solve it. Nearly all the students were glossy eyed and...

Homework Statement fnd 1+i\sqrt{3}/1+i knowing sin ∏/12 cos ∏/12 Homework Equations The Attempt at a Solution Our teacher did not really teached me how to do it...

hello! we know that in every right triangle there are the sin, cos, tan etc equations how do we prove that these equations are valid? eg. how do we prove that the adjacent of an angle divided by the hypotenuse of the triangle is always the same for that given angle? thanks

In the course of solving the simple harmonic oscillator, one reaches a fork in the road. x(t) = A1Sin(wt) + A2Cos(wt) At this point, you exploit a trig identity and arrive at one of two solutions x(t) = B1Sin(wt+phi1) or x(t) = B2Cos(wt+phi2) Both of these are correct solutions...

Hi, My Complex Euler stuff is a bit rusty but I'm working on a problem (that I won't mention here) but I'm after an explanation as to how: Sin (theta) = 3.08 and so Cos (theta) = -i*2.91 What's throwing me is that I know Sin can only have a max at 1 trigonometrically (obviously) so I'm...

Homework Statement Find the second derivative of sin y+cos y=x, giving your answer in terms of x. Homework Equations Implicit derivatives The Attempt at a Solution ##\sin y+\cos y=x## ##\cos y \frac{dy}{dx} -\sin y \frac{dy}{dx}=1## ##\frac{dy}{dx}=\frac{1}{\cos y-\sin y}##...

Homework Statement Find the amplitude, period, phase shift, and vertical shift Homework Equations y=- 1/2sin [3 (x-∏/2)] -2 The Attempt at a Solution amp = -1/2, vertical shift is 2 down y-axis. I can't get the period and ph. shift.

Homework Statement Find \sin^{-1}(-2) by writing [tex]sin w = -2[/itex] and using the rectangular representation of \sin w Homework Equations Rectangular representation of \sin w The Attempt at a Solution I think my biggest problem here is I have literally no idea what the...

Homework Statement lim (-x + sin(sinx))/(x(-1 + cos(sinx))) x-> 0 Homework Equations sinθ/θ=1 as θ-> 0 Squeeze Theorem? The Attempt at a Solution Well I've tried doing L'Hopital's rule, but to no avail. Each subsequent derivative just makes the equation nastier and more convoluted...

As the title inquires, I am curious as to how or why the Sin function represents y coordinate on the unit circle.

Homework Statement In the figure the three particles are fixed in place and have charges q1 = q2 = +e and q3 = 2e. Distance a = 6.00 µm. What is the magnitude of the net electric field at point P due to the particles? Homework Equations E = k*q/r^2 The Attempt at a Solution I...

Hello. This is part of a solution but I don't understand the underlined part. Why is it equals to 0?

Problem statement Solve each equation over the domain theta greater than or equal to 0, less than or equal to 2 pi: Sin theta= sin theta tan theta Revelant equations Problem statement I divided it by sin theta to get tan theta equal to 1. Tan theta=1 can occur in the first and third...

Mellin transform of sine Define the Mellin transform as $$\mathcal{MT}\{f(t)\}=\int^\infty_0 t^{z-1} f(t) dt$$ where $$z\in \mathbb{C}$$If the transform exists , it is analytic in some vertical strip $$a<\mathrm{Re}(z)<b $$ in the complex plane Find the vertical strip of $$\mathcal{MT}\{...

Homework Statement What is arcsin(√2)? The Attempt at a Solution sin-1(√2)=a+bi sin(a+bi)=√2 ...expressing as hyperbolic sin function: -i*sinh(-b+ai)=√2 sinh(-b+ai)=-(√2)/i ...using the definition of the sin hyperbolic function: (e-b+ai-eb-ai)/2 = -(√2)/i...

Hi, take the function I(m,n) = Integral from 0 to 1 of sin(m*pi*x)*sin(n*pi*x) over dx depending from n and m, being +-1, +-2, and so on. If I use sin(x)sin(y)=1/2(cos(x-y)-cos(x+y)) I get sin^2(n*pi*x)=1/2-1/2cos(2n*pi*x) or I(n,n)=1/2 because the integral of cosine over full...

Homework Statement i have solve 7sin(2x)-13sin(x)=0 for all solutions 0≤X<2p I used the double angle formula for sin(2x)=2sin(x)cos(x) The Attempt at a Solution I'm getting stuck near the end 7(2sin(x)cos(x)-13sin(x)) 14sin(x)cos(x)-13sin(x) now I am stuck

In finding Cn, I arrived at a different answer. I got an extra factor of (1/i) instead, which came when you do the integral of each exponential with respect to t; so you get a factor of 1/i(1-n) and 1/i(1+n) respectively.. Did they intentionally leave that out?

Homework Statement 20sin(t)cos(t)=-4cos(t) Homework Equations The Attempt at a Solution I added the cos to the other side but I am kind of stuck what to do. My instructor never really went over this well enough. Ugh..

Find (a) sin ∅, (b) cos ∅, and (c) tan ∅ for the given quadrantal angle. If the value is undefined, write “undefined.” My quadrantal angle is -450° Sin = opp/hyp Cos= adj/hyp Tan= opp/adj I drew a graph and put the angle -450° in the 3rd quadrant because both x and y are negative and I...

3. Fourier sin series for f(x) = 1, 0 < x < pi is given by 1 = 4/n E 1/ (2n-1) times sin (2n-1) x, (0 < x < n). Using this, find the Fourier sinc series for f(x)= 1, on 0 < x < c where c > 0. Then find the Fourier series for g(x), x > 0 where g(x) = 1, 0 < x < c, -1, c < x < 2c, g (x + 2c)...

Homework Statement Evaluate derivative of (sin sq. root x) w.r.t x? Homework Equations Limit Δx--> 0 (sin√(x+Δx) - sin(√x)) / Δx The Attempt at a Solution i couldn't operate it from here... Δy = (2cos((√x+Δx) + (√x)) . sin((√x+Δx) - (√x)) / Δx...?

lowest value that can get the "sin" and the "cos" Sorry for my stupid question,but I forgot them. What is the biggest and the lowest value that can get the "sin" and the "cos" Thanks!

Homework Statement A transverse wave travels on a string whose mass density is

 kg/m. The displacement (in meters) is given as a function of time and position as:     D(x,t) = 1.5sin(3x-24t+90°)
What is the velocity and direction of the wave? What is the speed of...

from this equation i get the amplitude is 8 cm, it's a sine function so i guess it has to be a harmonic oscillation i haven't had physics in a while so not really getting anywhere -i need to know T (time for one oscillation) -the frequency f which is 1/T -Vt and At equations, i know i...

How to find the integral of sin x dx? $$\int sin x dx=?$$

hi every one .. i have some question 1 - why the value of exp = 2.71 ?? were from they get this value ? any derive or rule ? 2 - who i can fiend the value of ln and exp and sin or cos without using calculator ? like cos 56 sin 28 ?? or ln 24 ? exp 33 ? without using...

Homework Statement Hey all, I am working through a derivation that my professor gave me to do and I am having trouble understanding one of the formulas that he gave me, namely: "EM waves can be described as: E(x, t) = Eosin(2πx/λ)*sin(2πc/λ)" The the Eo*sin(2πx/λ) term makes sense to...

What differente does it make? As far as I can see it, the limit definition of a derivative shouldn't be affected by the fact that x is expressed in radians or degrees...

Hi all I am trying to go through and understand the derivation of \[X_{c} = \frac{1}{j\omega C}\] Where $X_{c}$ is capacitive reactance in ohms, $\omega$ is the angular velocity or $2\pi frequency$ and $C$ is capacitance in FaradsTo start with we already have $I=C\frac{dv}{dt}$...

Why do some wave equations use sinθ and others cosθ? Does it make a difference when calculating properties such as wavelength and wave number? For example: y(x,t) = Asin(ωt+kx) y(x,t) = Acos(ωt+kx)