Cosine Definition and 337 Threads

For problem: See Attachment I've never done a problem of this sort and it's proving to be much more difficult compared to the other problems I have had assigned to me. I'm not entirely sure which formulas to use but I've been playing with the following: Length of Arc = r\theta A = \pir^2 C =...

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?

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...

Homework Statement Part (b): Find the perturbed energy. Homework Equations The Attempt at a Solution I've solved everything, except part (b). I got an answer of 0 for part (b) for all orders, which is kind of strange, as one would expect some perturbation. \Delta E_n = \langle \psi_n...

Hi, I am supposed to use residue calculus to do the following integral $$\int_{0}^{2\pi}\frac{1}{a+b\cos( \theta) } \mathrm{d}\theta$$ for |b|<|a| i have paremetrise it on $$\gamma(0;1)$$ that is $$z=\exp(i\theta), 0\leq\theta\leq2\pi$$ and obtain the following...

This is about wave reflection and transmission. For an infinite string with a density change at x=0, consider an incident wave propagating to the right from x = -∞. The most general form is W = A cos(w(t-x/c)+θ), with amplitude A, angular freuqency w, time t, distance x (from origin), wave...

Hello, ∫|cos(px/2)|dx between [0,2] I encountered this rule. How does this apply to other intervals of say [3,4],[7,9] etc. Are the numbers both halved? so [3,4] becomes [1.5,2] etc? Also, does this rule apply to all symmetrical functions? Thank you, Tim

Homework Statement a) Show that the Fourier Cosine Series of f(x)=x,\quad 0\leq x<L is x ~ \frac{L}{2}-\frac{4 L}{\pi ^2}\left[\left(\frac{\pi x}{L}\right)+ \frac{\cos\left(\frac{3\pi x}{L}\right)}{3^2}+\frac{\cos\left(\frac{5 \pi x}{L}\right)}{5^2}+\dots\right] b) use the above series to...

Find the Fourier cosine series of $$cos(x)$$ from $$x=0 ~to ~\pi$$ Here the Fourier series is given by $$f(x)=\frac{1}{2}a_0+\sum_{n=1}^{\inf}a_n cos nx dx$$ where $$a_n=\frac{2}{\pi}\int_0^\pi f(x)cos nx dx$$ I am facing problem to solve it. I am getting $$a_0=0$$ and $$a_n=0$$ so the Fourier...

Homework Statement What would be the limit of {cos(m!*pi*x}^{2n} as 'n' and 'm' go to infinity along with proof? Also x is real. I have no clue as to how to start the question. Please help! Thanks. The Attempt at a Solution I tried to write the original function as...

Homework Statement The cosine of a vector is equal to the opposite over its magnitude. Homework Equations The attempt at a solution[/b] the cosine is the ratio of the adjacent to the hypothenuse this is why i say it "came' is incorrect.

Here is the question: I have posted a link there to this thread so the OP can view my work.

Homework Statement Consider the inner product $$\frac{1}{2\pi}\int_0^{2\pi} \left(\frac{3}{5 - 4\cos(x)}\right) e^{-ikx} dx, \quad k \in \mathbb{Z}, \quad x \in \mathbb{R}.$$ Homework Equations Is there a method to solve this without using the residue theorem, e.g. integration by parts...

Phase modulation is a system in which the amplitude of the modulated carrier is kept constant, while its phase and rate of phase change are varied by the modulating signal. By the definition of phase modulation, the amount by which the carrier phase is varied from its unmodulated value, called...

My online physics course is using cosine law to find the net forces on objects. My question is to do with the equation, at first it shows it as : c^2=a^2+b^2-2ab cosC. From there, it changes to: c=[a^2+b^2-2ab cosC]^1/2. How and why does this work? Why isn't a square root involved in the...

Homework Statement I need to prove or show that this n-rowed determinant which corresponds to cosine multiple angle formula is in fact true using induction. The Attempt at a Solution First let ##a = \cos \theta## and suppose I have this n by n determinant. $$ \begin{vmatrix} &a &1 &0& \\...

Just for clarification... If I take the cosine similarity of two vectors and i get an answer of 1, then bother vectors are equal and the same. If I do the same again with another two vectors and get an answer of 0, then the vectors are at an angle of 90 degrees to each other and...

Homework Statement 9cos(2t)=9cos2(t)-4 for all the smallest four positive solutions Homework Equations The Attempt at a Solution I've factored it and pulled out 9cos(t) and made that = u so i have u2-2u-4 That factors to 3.23606 and -1.236 Next i added 9cos(t) back in...

How many (unordered) sets of pairwise distinct real numbers $$\{t_1,t_2,t_3,t_4\}$$ all between 0 and $$2\pi$$ are there such that in some order they satisfy the following system: $$\begin{align*}\cos(2t_1)=4\cos(t_1)\cos(t_2)\\ \cos(2t_2)=4\cos(t_2)\cos(t_3)\\ \cos(2t_3)=4\cos(t_3)\cos(t_4)\\...

I have to plot a bunch of cosine waves and then add them up but my problem is that each indiviudal wave looks really weird when I plot and not like a cos wave. The program runs and plots the final result but I'm not sure how accurate it is because when I plot each individual cos wave I know it...

Homework Statement The problem: Justify the following equalities: \cot x = i\coth (ix) = i \sum^\infty_{n=-\infty} \frac{ix}{(ix)^2+(n\pi)^2}=\sum^\infty_{n=-\infty}\frac{x}{x^2+(n\pi)^2} I am trying to figure out how to start this. When I insert the Euler identity of \coth (using...

2. Fourier cosine series correspondence for f(x)= x, o < x < pi given by x ~ pi / 2 - 4/n, E infinity on top and n=1 on bottom. cos (an-1)/x / (2n-1)squared, (0 < x < pi). Explain why this correspondence is actually an equality for 0 is less than or equal to x and x is less than or equal to...

The N real numbers x0, ..., xN-1 are transformed into the N real numbers X0, ..., XN-1 according to one of the formula by DCT. I would ask what is the benefit and why should we do that?

Hello my friends, I posted this picture as a proof of the Cosine Rule in another thread, however after having a closer look at it, I believe it is incomplete. It works by drawing a segment from one of the vertices so that this segment is perpendicular to one side of the triangle, and then...

Partial Derivatives Hi all I was wondering if anyone could help me with this problem. I have a triangle that has a = 13.5m, b = 24.6m c, and theta = 105.6 degrees. Can someone remind me of what the cosine rule is? Also (my question is here) From the cosine rule i need to find: the...

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...

Here is the question: Here is a link to the question: Help with precalculus! Sum or difference formula? - Yahoo! Answers I have posted a link there to this question so the OP can find my response.

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...

Hi. I have a doubt about an exercise in a book of optics. It's about Youngs double slit experiment. The exercise asks to apply the law of cosines. That part was easy, you can see in the diagram, alpha is the complementary angle for theta, it goes straight forward. What I got is this...

Hi, I've been listening to the podcast "Neuroscientists Talk Shop" and heard some participants repeatedly refer to something called "cosine tuning" in relation to predicting the efferent reactions to certain clusters of neurons (e.g. a simian moving in a certain way). [sorry if that's...

Homework Statement -\frac{1}{2}[cos(\frac{\pi+\pi n}{\pi+\pi n}) + cos(\frac{\pi-\pi n}{\pi-\pi n})] Homework Equations cos(u)cos(v) = \frac{1}{2} cos(u+v)+cos(u-v) The Attempt at a Solution I am attempting to use the above trig function to simplify the first function, but I can't seem to...

I'm having trouble understanding when to use sine or cosine in my physics problems for example I got this from one of the lectures off youtube and I know why they are using sine and cos because it is at an angle but I'm rotating the angle to understand why it is mgcosbeta and why the other is...

Hello, I got problem solving $$\lim_{x \to 0}\frac{\cos(x)-1}{\sin(x)}$$ I do not really get any progress, I would be glad if someone could give me tips!

Homework Statement I just have to prove the well known identities: \cos(\alpha + \beta)=\cos(\alpha)\cos(\beta)-\sin(\alpha)\sin(\beta) \sin(\alpha + \beta)=\sin(\alpha)\cos(\beta)+\cos(\alpha)\sin( \beta) But the thing is that I've to use the Taylor power series for the sine and cosine...

Homework Statement Express 3sin(ωt) + 2cos(ωt) in the form Rsin(ωt + α) AND verify the resultant function is the same frequency as 3sin(ωt) and 2cos(ωt) Homework Equations R = √a2+b2 α = arctan(b/a) The Attempt at a Solution My attempt using the equations above produces...

Do anyone know what properties of cosine function should we use? and the method to use it? kinda blur...

Ordinarily in mathematics, when you want to define a function, it is without reference to geometry. For instance the mapping f:ℝ→ℝ x→x2 And though I don't know much about mathematics I assume you somehow proof that the function is well defined for all numbers, check if the derivative exists and...

It's always a brat to differentiate/integrate it due to the sign change. Why can't it be more like sine?

1. Homework Statement Find the cosine of the angle between the normals to the planes: x+y+2z=3 and 2x-y+2z=5 2. Homework Equations [/b] x+y+2z=3 and 2x-y+2z=5 3. The Attempt at a Solution All I know is cos θ= V * W / ||V|| ||W||

\lim_{n\to\infty} \left (\lim_{k\to\infty} \cos (\left| n! \pi x\right|) ^{2k} \right) = \begin{cases} 1&x \in \mathbb{Q} \\0& x \not\in \mathbb{Q}\end{cases} . How to prove it?

So here is my question, I understand how to derive the cosine rule from, both triangles acute and obtuse. My problem is the 3 formula you get from this equation. When I derive from a triangle I get the formula: c^2=a^2+b^2-2abcos∅ so how do you derive the other two formula, I read that...

Homework Statement \int { { cos }^{ 2n+1 }(x)dx } Homework Equations { cos }^{ 2 }+{ sin }^{ 2 } = 1 The Attempt at a Solution i got to here: \int { { (1-{ sin }^{ 2 }(x)) }^{ n }d(sin(x)) } Any help would be appreciated!

Homework Statement It isn't a homework problem per se, but a curiosity a stumbled upon when trying to solve a physics problem (I was trying to calculate the angle I would need to do less work possible, while moving the box). The equation I found is: f(\theta)=\cos(\theta)+...

Homework Statement Find the cosine Fourier transform of the function f(t)=e-at Homework Equations The Attempt at a Solution F(w)=(2/π)0.5∫dt e-atcos(wt) The integral is from 0 to +∞ Using euler's formula I got the result F(w)=(2/π)0.5( eit(w-a)/i(w-a) - e-it(w+a)/i(w+a)...

I have to find the cosine of the following: | 1 0 | | 2 2 | This is a 2 by 2 matrix. I have been reading my linear algebra book for awhile now, and theirs no information at all on how do to something like this. Not sure how to find the cosine of a matrix. Could not really find any pages...

I have manged to get my answer down to the first line in the picture but I have tried all ways and can't seem to simplify it to the second line. Thank you

I am currently doing a trig question and trying to find the location of the acute angles of cosine inverse and I am just wondering if cosine inverse follow the cast rule? In other words would it be positive where cos would be positive or not?

What does "phase of the motion in terms of cosine displacement" mean? I'm getting tripped up on the wording of this homework question. Homework Statement Measured acceleration: An accelerometer has measured the simple harmonic motion shown in the image below. Homework Equations You...

Homework Statement cosθ = 1.316581Homework Equations cos-1cosθ = θ // if and only if 0\leqθ\leq1 The Attempt at a Solution This problem is actually the result of an attempt at a solution to solve an even larger problem (SAS triangle specifically). I need to know how to restrict the cosθ...

Hi, all I am looking into inverse cosine operations. I have a question like follows: Let x and y be two variables of degrees, how to separate equation arccos(x+y) into an equation that contains x and y separately? Such as arccos(x+y) = f1(...x) + f2(...y)? Thank you very much for your...