Cosine Definition and 337 Threads

Evaluate the following limit: \lim_{n\rightarrow \infty}\frac{1+\cos(\frac{x}{n})+...+\cos(\frac{n-1}{n}x)}{n}

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

I have a cosine function, namely the function for oscillation x=A cos(wt). I want to separate the t out here, so I can solve for it. My teacher gave the the answer to be t= (arccos (x/a)/2pi)*T, but I can't quite see where he came up with that. Would anyone be as kind as to give me a more...

Homework Statement Find the Fourier cosine series for f(x) = cos x, 0 < x < Pi EDIT: I believe we are talking about a half-range extension.. Homework Equations Fourier cosine series: f(x) = a0/2 + Sum(n = 1 to infinity) (an * cos (nx)) where a0 = 2/L * integral (x = 0, x = L)...

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...

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...

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?

Homework Statement integral 1/(a+cos(t))^2 from 0 to pi. Homework Equations cos(t)=1/2(e^it+e^-it) z=e^it dz/(ie^it)=dt The Attempt at a Solution int dt/(a+cos(t))^2 = int dz/iz(a2+az+az-1+z2/4 +1/2 +z-2/4) so with these types of problems I normally can factor this guy...

Homework Statement Two vectors of lengths a and b make an angle θ with each other when placed tail to tail. Prove, by taking components along two perpendicular axes, that the length of the resultant vector is r=√(a^2+b^2+2abcos θ ) Homework Equations Would this be correct? How would you...

The problem is finding the points of intersection for two given functions. f1=sin(-\pi*x) f2=1+cos(-\pi*x) I've plotted the functions using Maple. http://dl.getdropbox.com/u/12485/plot.png And I'm quite certain that to find the points of intersection, I have to set f1=f2 which...

1.x = rcos(a)cos(a) x is known r is known I can't seem to get this! x = -2 r = 7 therefore -2/7 = cos(a)*cos(a) so.. -2/7 = cos^2(a) i know cos^2(a) = 1 + cos2a / 2 -2/7 = 1 + cos2a / 2 so -4/7 -1 = cos2a I cannot take cos inverse of this value since it is...

Homework Statement Find the sum of the series s(x) = 1 +cos(x)+ (cos2x)/2!+(cos3x)/3!... Homework Equations The Attempt at a Solution

I have a few questions: What’s that formula called? The correlation formula? Is cos^2 the formula for only particles with spin=1 like photons? If so, what’s used for electrons (1/2 spin). Also, cos^2 seams funny to me since it returns 1 for 0 and 180 degrees. Zero I can understand since you...

Hello, I have a quick question relating to Lambert's cosine law for diffuse reflection. My understanding of the law is that given an isotropically illuminated surface, the reflection distribution goes with the cosine of the zenith angle. Now my question is whether or not that law holds for...

Homework Statement I make the product \cos(x)\cos(5x) a sum of two cosines. I think this is called linearizing but please correct me if I'm wrong. (I need it to find the n-th derivative of that function). Homework Equations The Attempt at a Solution I know the answer is...

Homework Statement given 2 functions f and g related by a cosine transform g( \alpha ) = \int_{0}^{\infty}dx f(x)Cos( \alpha x) then if the integral \int_{0}^{\infty}dx f(x)exp(cx) exists for every positive or negative 'c' then should it be equal to \int_{0}^{\infty}dx...

Homework Statement Just wanted to check if I did the Fourier transform of a somewhat long function correctly Homework Equations f(x) = (1+cos(\frac{2pix}{w}))rect2(\frac{x}{w}) they're not convolutions, just a modulation equation used in imaging studies 'rect' is rectangle function...

Homework Statement (cos(x))^p \leq cos(px) 0\leqx\leqpi half and p, 0\leq(not equal) p \leq(not equal) 1 i need help, if some one can tell me how to started, what should i used i will really apreciate it! (sorry for my english :confused:) Homework Equations The Attempt at...

Homework Statement I have 1.805cos(2pi / 12.165x) +3.125 as the function of tidal data. However I need to use another function, superimpose, to more accurately graph the data for the tides. And yeah I'm pretty lost... Does the next function have to be something to do wit the moon and its...

I'm having a bit of trouble working out the cosine function for the data I have on tide charts. Homework Statement I need to put the data provided into the cosine function y=acos(nx-b)+c Morning average high tide: 5.137 metres Morning average low tide: 1.29 metres Afternoon average high...

I have a question on complex analysis. Given a differential equation, \dfrac{d^2 \psi}{dx^2} + k ^2 \psi = 0 we know that the general solution (before imposing any boundary conditions) is, \psi (x) = A cos(kx)+B sin(kx). Now here's something I don't quite understand. The solution...

Relative to a fixed origin O, the point A has position vector 4i + 8j – k, and the point B has position vector 7i + 14j + 5k. (a) Find the vector A to B. (b) Calculate the cosine of OAB. (c) Show that, for all values of t, the point P with position vector ti + 2tj + (2t - 9)k lies on the...

Hello, I have attached the problem that I am referring to. Basically I have a particle traveling on a path defined by a cosine function and I want the equations of motion with respect to the inertial system, if the particle is under the influence of friction and gravity. I have calculated...

So...a cosine wave when shown in the frequency domain is represented by a 1/2 magnitude vector at the positive frequency and a 1/2 magnitude vector at the negative frequency. I am surprised by this because I cannot understand why a vector of magnitude 1 at the positive frequency of the cosine...

soine cosine rule I have a question for you, I came across this question while revising for my exam on monday if anyone can answer this I'll be very impressed. Two different trangles ABC have AB=5cm, AC=3.2cm and angle ABC=35degrees calculate the difference between their areas.

Hi Guys/Girls, I have a maths exam tomorrow and there is a chance I could be asked to prove the cosine rule or sine rule. Well I have a simple proof of the sine rule but cannot find a simple one for the cosine. They all seem very advanced. Would anybody have a straightforward proof for...

Homework Statement 1. Homework Statement A river is 2 km wide and flows at 6 km/h. A motor boat that has a speed of 20 km/h in still water heads out from one bank perpendicular to the current. A marina lies directly across the river on the opposite bank. Use Geometric Vectors to solve...

Homework Statement Calculate \sum_{n=2}^{\infty}\frac{1}{n^{2}-1} with the "standard" method and with the method of the partial fraction decomposition of the cosine. Homework Equations \pi\cot\pi z=\frac{1}{z}+\sum_{k=1}^{\infty}\frac{2z}{z^{2}-k^{2}} The Attempt at a...

If cosine is equal to -12/13... Find sine and tangent in Quadrant If cosine is equal to -12/13... Find sine and tangent in Quadrant Two... What is the answer??

It is a simple math question, but I am stuck. The law of cosines is R^2=h^2 + r^2 - 2 h r cos (theta). Theta is of course the angle facing R. To differentiate, I first set r^2 - 2hr cos\Theta+ (h^2-R^2) = 0 2 r \dot{}r - 2 h cos\Theta \dot{}r + (h^2-R^2) = 0. Is there any...

Homework Statement This is part of a larger engineering problem, I have reduced it to this mathematical equation, which should be simple, right? I need to find when the following EQ has Maximum's (in terms of x)...

To show that cos-1(-x)-cos-1(x)=2sin-1(x) I tried take x= sina taking cos of the whole equation cos(cos-1(-x))-cos(cos-1(x))=2cos(sin-1(x)) now we have to prove : -x-x=2cos(sin-1(x)) LHS: -2x=-2sina=2cos(a+pi/2) RHS: 2cosa Iam not sure how to proceed further..can anyone help me...

[SOLVED] Finding sine and cosine formulas Homework Statement If sinx/siny = 1/2 and cosx/cosy = 3 prove: sin (x + y) = 7/3 sinx cosx Homework Equations sin (x + y) = sinx cosy = cosx siny The Attempt at a Solution Can someone please give me a hint so that I can start? Thanks.

I need to normalize the following wave function: psi= Cexp(-abs(x))exp(-iwt)cos(pix) I know that when squaring it, the time dependent part drops out, which is good, but what I seem to be left with is Psi^2=C^2exp(-2abs(x))cos^2(pix) Which seems like a fairly complicated integral to...

I need help on graphing cosine and sine functions. i know how to read a graph and come up with the equation but i don't know how to do it the other way around. i want to be able to graph something like y=-2+2cos0.5x

I'm not getting the right answers for sine, cosine and tangent functions. I have no idea why this is.

[SOLVED]Sine, Cosine and Tangent Trig Help I'm in 10th grade, I was just doing my homework when this dawned on me: How would one find Sine, Cosine and Tangent without a calculator. So if I am stuck in the desert with a stick I could find the Cosine of 73º by stick and sand method...

Homework Statement There is a right angled triangle, with the following angles, a, b, and 90deg. If a < b, how many different values are there among the following expressions? sin a sin b, sin a cos b, cos a sin b, cos a cos b Homework Equations The Attempt at a...

I am having trouble understanding when to use sine and cosine to find x and y components. I know that its not always going to be the same (ex. you won't always use cosine to find x component.) Any input would be appreciated!

Hi I would really appreciate it if anybody could lead me in the right direction on this one... |A| = |B| |A+B| = 100|A-B| I need to find the angle between A and -B for the statement to be true. Using cosine laws I've come up with the following eqn: |A+B| = 100|A-B| 2|A|^2 + (2|A|^2)(cosx)...

What is a wavefront? Huygen's principle says that every point on a wavefront acts as a source of wave with the same speed. Now I am not asking you what that means, but i don't understand what a wavefront is. Is that like a circle? But wave is usually like a sine or cosine graph, so what's the...

Homework Statement Prove the identity: Cosh(x) + Cosh(y) = 2Cosh[(x+y)/2]Cosh[(x-y)/2] Homework Equations Cosine sum-to-product http://library.thinkquest.org/17119/media/3_507.gif The Attempt at a Solution Can you use the same formula for Cosine sum to product for hyperbolic...

I've stumbled upon what might be a geometrical interpretation of Taylor's series for sine and cosine. Instead of deriving the Taylor's series by summing infinite derivatives over factorials, I can derive the same approximation from purely geometrical constructs. I'm wondering if something...

expand the function y=sinx in a series of cosines in the interval (0 to 180) i want to know only the value of f(x) for solving this.what is the value of f(x).

Homework Statement Solve cosz = 2i , z\in \mathbb{C} The Attempt at a Solution e^{iz}+e^{-iz} = 4i t=e^{-z} t+t^{-1}=4i \Rightarrow t^{2}-4it+1=0 t = (2 \pm \sqrt{5})i log(e^{-z}) = logt z = x + yi;x,y \in \mathbb{R} log(e^{-z}) = log(e^{-y+ix}) = -y +xi +...

Homework Statement can som1 please give me an idea where to start with this integral. integral of: cos (2t) x e^2t thanx Homework Equations The Attempt at a Solution

Hi, I recall that when you use the cosine rule you can sometimes come out with 2 answers (somthing to do with cos graph?). I can't qutie remeber and I've looked through my books and I can't find it. I can use the rule to calculate one side or angle, but when do you get 2 answers? Can someone...

I'm having a lot of problems with this topic. I know what the sine, cosine and tan graphs look like. one question i come across fequently is "given that sin 30°, what is a) sin 150° b) sin 330°. - i can work it out on a calculator but the questions on a non-calc paper. I am presuming it's...

Homework Statement Hello, I'm trying to find the area enclosed by sine the cosine function on the interval 45 degrees and 225 degrees, my problem is i get a negative number after i do the integration, my answer is -2 root 2. here's what i did, sin(x)-cos(x)dx after integrating...

I am rediscovering my long lost "A" level maths and have been having lots of fun working on puzzles. Unfortunately, I seem to have hit something of a wall in the following simple expression that is repelling every attack I launch: f(x)=Sqrt(1+kcos(x)) I have tried substituting x=arccos(w)...