Cosine Definition and 337 Threads

Homework Statement From angles pi minus theta1 to pi plus theta1, what is the integral of cosine of 2 theta times d theta? Homework Equations The Attempt at a Solution When I evaluate this definite integral from pi minus theta1 to pi plus theta1, I get positive one half sine of...

Demontration of: cos(x)² = 1 \overline{1+tan(x)²} Anyone know? If you don't understand: cos(x)² = 1/1+tan(x)²

Homework Statement How many terms of the taylor series of the cosine function about c = 0 are needed to calculate cosine 2 to an accuracy of 1 / 10000 The Attempt at a Solution I have said that |Rn(2)| = |cosn+1(a) 2n+1/(n+1)!|<2n+1/(n+1!) Now i can't do it ...

Homework Statement I have a problem, it's last major grade for my pre cal, it's about six flags and here's the information: H(min)(Trough): 3.ft H(max)(crest): 32 ft b= 10 ft period = 160 ft write a cosine equation to model of the wave Assuming still that the leftmost crest intersects...

If I modulate a pulse X(t) with a.) a sine wave or b.) a cosine wave, I have the frequency spectrum expressions a.) \frac{1}{2j}[X(f-f_0)-X(f+f_0)] b.) \frac{1}{2}[X(f-f_0)+X(f+f_0)] When I plot these for a pulse, I see a difference in the magnitude spectrum, but I should not expect...

Hi, please look at the following equation. \frac{3}{16}\frac{\nu_{Q}^{2}}{(1+K_{iso})\nu_{0}} \left(\frac{7}{2} \cos^{4}\theta - 3\cos^{2}\theta + \frac{5}{6}\right) In the paper I am reading, this is simplified considering the isotropic average of a cosine function to...

I have yet to see or understand the benefit of knowing the cosine and sine sum and difference of two angles identity... can someone please explain why you would want to break up one angle into two angles... then solve from there... does not make sense to me... just use a calculator.

Homework Statement f(t)=1-t ; 0≤t≤\pi Homework Equations The Attempt at a Solution a_{0}=\frac{1}{2}\int_{0}^{2}\left( 1-t\right) dt=0 a_{n}=\int_{0}^{2}\left(1-t\right ) cos(\frac{n\pi\left t \right}{2}) dt = \frac{4}{(n\pi)^2}(1-(-1)^n) Ans that is given to me is: \frac{2}{\pi} +...

Ok... so I had this down and now I am all confused ;/ I am not posting in the homework sections because its not for homework although I will gie an example of a problem... I just want to understand why/how they use these to find the force/tension... Example: A 20 kg loudspeaker is...

How do i distinguish between a cosine and sine function simply by looking at the graph? Usually its easy because the graph for the base sine and cosine functions have certain distinctive features(like cosine function intercepts the y-axis at 1 usually) and the sine function hits the origin(0,0)...

Homework Statement In Example 3 under Theorem 2.5 of Apostol's Calculus Volume 1, I don't understand how the final formula on the right is obtained.Homework Equations The identity cos 2x = 1 - 2 sin2 x implies sin2x = 1/2(1 - cos 2x) so, from Example 2, we obtain: \int^a_0\,sin^2\,x\,dx =...

How Do i find the zeros for this particular sine function? y=asin(k(x-d))+c when we are given a K value i know how to find the zero but when we are not, i don't know how to find the zero(Atleast after everything has been horizontally, and vertically shifted and streched) y=2sin(x-30...

I was asked to draw the graph of y=cosx-2 This equation means the graph of y=cosx is shifted 2 units down correct? (Since -2 is the C value because if it were the d value in y=acos(k(x-d))+c it would be in degrees, so we shift each y coordinate down 2 units, or subtract the y value by 2, i...

Graph the function y=cosx-2I have already graphed this, there are several methods to solve this, i opted to use table of values to find all the coordinates to y=cosx, then moved all the y coordinates of each point 2 units down, and the y int was at -1...would this method result in the correct...

I just learned about hyperbolic functions in my calculus class, and though my professor attempted to explain the use of hyperbolic functions, he really did not go very far into it, just providing a weak example ("If two people are holding a chain, cosh(x) factors into how much the chain...

Homework Statement Find the linearization L(x) of f(x) = cos(x) at a = π/2 Homework Equations L(x) = f(a) + f'(a)(x-a) The Attempt at a Solution I just want to make sure I did this correctly: L(x) = cos(π/2) + -sin(π/2)(x-(π/2)) L(x) = 0-1(x-(π/2)) L(x) = -x + (π/2)...

Hi all, Hope some here can help me with this math problem. Given, y1 = ax^2 + b. y2 = cos (y1). where a and b are constants. Is y2 periodic with respect to x.? Visually using example grpah, seems to be periodic. How do u find the exact period of such a function? Thanks in advance...

Homework Statement See figure attached for problem statement as well as my attempt. Homework Equations The Attempt at a Solution I'm not fully convinced I've done the sketch of the cosine series correctly or not, are there any mistakes? Also, when solving for, a_{n} I changed...

Can the cosine law be used on right triangles as well as oblique triangles?

Homework Statement What is the importance of knowing how to express trig ratios in terms of sine, cosine, tan, cosec, sec, or cot? Homework Equations The Attempt at a Solution

Hi. I have been experimenting a little to come up with the following "conjecture" \int_0^{2\pi}d\phi f(a+b\cos\phi)\sin\phi=0 where a and b are arbitrary constants and f(x) is any function. Is this true? I guess it can be shown by expanding f in a power series of cosines?

Homework Statement The function f(x) is defined on the interval 0<x<L by f(x)=x. It can be represented by the Fourier cosine series f(x) = a_0 + sum a_n cos(n*pi*x / L) Find its Fourier coefficients a_0 and a_n. Homework Equations Multiply both sides by cos(n*pi*x / L) and...

Homework Statement Find simple formulas for 1+ cos(θ) + cos(2θ) + cos(3θ) + ... + cos(nθ) and sin(θ) + sin(2θ) + sin(3θ) + ... + sin(nθ) The Attempt at a Solution It's not really a homework question, but more for making a problem that I'm trying to solve a little bit more simple...

Homework Statement limit as t-->10 of cos (1/10-t) Homework Equations The Attempt at a Solution Obviously we can't substitute in t = 10 or it would be undefined, so how do we do this. Is there an inequalitly that I haven't considered?

Homework Statement Find the period of the signal x(t) = 2 + 4cos(40Pi*t) + 3cos(60Pi*t) + 4cos(120Pi*t). Homework Equations The Attempt at a Solution The fundamental frequency (fo) = 10 Hz, since that's the greatest common factor of all the frequencies of the cosine signals. So...

I've attached the multiple choice question. The first time round that I did it, I simply just did a phase shift of the whole graph by pi. Basically I just translated the whole graph by pi, resulting in option (D). However, it later came to my attention that by continuing to draw the...

hi every one, i have one doubt i studied abt trignomentry. there finding the triangle angle or side of the triangle using sine function. if we are taking right angle triangle sine A = opp/hypo, cos A = adj/hypo and tan A=opp/adj. here we are finding angle for A only why we are having three...

sin x = 0.5299 cos x = 0.8480 Without using inverse cos or inverse sin, is it possible to calculate the angle?

a.cos(wt) + b.sin(wt) = M.cos(wt + ϕ) Can you give me M and ϕ in terms of a and b?

Homework Statement I need to rewrite this equation as a function of y. would love some help since i failed on the right side of the equation. v= [πr(3R-y)y²]/3R + L√[(2R-y)y(y-R)+R²cos^-1(1- y/R)] i mean is it even possible to get y out of there, with inverse cosine and all? Thanks in...

So in Analysis I we explained the convergence of cos to a fixed value by Banach's contraction theorem. But is the cos a strict contraction? Is that obvious? (What is its contraction factor?)

Homework Statement I need to fit a curve using cosh to a hyperbola with a vertex of (0,0) and a point at (4,7). The scanned worksheet can be found here http://img519.imageshack.us/i/scan0001gu.jpg/" http://img192.imageshack.us/i/scan0002uz.jpg/" Homework Equations y=a cosh...

Homework Statement The problem is as follows: Let f be a real valued function that is Riemann integrable on [a,b]. Show that \lim_{\lambda \rightarrow \infty} \int_{a}^{b} f(x)\cos(\lambda x)dx = 0 . Homework Equations I am freely able to use the fact that the product of...

I got this question wrong and I'm hoping someone can explain to me where I went wrong. In a triangle... angle A = 350 side b = 7 cm side c = 3 cm I need to find side a which is the side opposite angle A. The formaula to use is -a2 = b2 + c2 - 2bc cos A so, with the figures plugged...

Homework Statement Q'' + 100Q' +50000Q = 4000cos(100t) i found the general solution to be e-50t[Acos(50sqrt19)t +Bsin(50sqrt19)t] but i have a problem with the particular solution i tried Cei100t did i try the wrong expression? because when i compared coefficients, i found...

Homework Statement ok so I am given that I(t) = A cos (w1 t)cos(w2 t) where w2<<w1 then I am asked to express I as the sum of two cosine functions with angular frequences P and Q which I have: I = A/2 (cosPt + cosQt) where P = w1+w2 and Q=w1-w2 Im then asked to evaluate the...

Homework Statement f(x) = sin(x) for 0\leqx<\pi. Extend f(x) as an even function . Obtain a cosine Fourier series for f. Homework Equations a_{0}/2 + \sum a_{n}cos(nx) The Attempt at a Solution So as far as I know, to extend sin(x) as an even function you have to make f(x)=-sin(x)...

Homework Statement Using the Fourier cosine series for \[f(x) = \left\{ \begin{array}{l} 1,x = 0 \\ 10,x = \pi \\ x,x \in (0,2\pi ) - \left\{ {0,\pi } \right\} \\ \end{array} \right.\], find a series that converges to \[\int\limits_0^{2\pi } {{x^2}dx} \] The Attempt at a...

Homework Statement Hi guys, I don't know if this should go here because it is an excerpt from a higher level problem. The part where I get stuck is when I try to add the cosine functions. Is there any way to add sine and cosine functions that have a scalar in front that cannot be factored...

Homework Statement 3 waves are represented by these 3 waves inteferring: cos(Θ-π), cos(Θ+π), 3cos(Θ)? cos(\theta-\pi), cos(\theta+\pi), 3cos(\theta). If I want to diagram these, does the cos(\theta-\pi) and cos(\theta+\pi), cancel each other out? Do I need to convert them to sine...

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 \...

Homework Statement cos(α − β)cos(α + β) = cos2α - sin2 β Homework Equations cos(α + β) = cos α cos β − sin α sin β cos(α − β) = cos α cos β + sin α sin β The Attempt at a Solution I worked out the LHS which makes it cos2α cos2β - sin2α sin2β=RHS Then, I'm stuck, however, i...

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

Homework Statement Three units vectors a, b, and c have property that the angle between any two is a fixed angle \theta (i) find in terms of \theta the length of the vector v = a + b + c (ii) find the largest possible value of \theta (iii) find the cosine of the angle \beta between a and...

Hi I have been working on a example and have worked it out as this Homework Statement f(x) = \( \left( \left \begin{array}{ccc}0 & \mathrm{for} & -\pi < x \leq 0 \\ cos(x) & \mathrm{for} & 0 < x < \pi\end{array} where f is defined on the interval ]-\pi,\pi[. Find the...

Homework Statement Pick any numbers that add to: x + y + z = 0 Find the angle between your vector \textbf{v} = (x, y, z) and the vecor \textbf{w} = (z, x, y) Explain why \textbf{v}\bullet\textbf{w} / ||\textbf{v}||||\textbf{w}|| is always -\frac{1}{2} Homework Equations Cosine...

Hi Everyone, I am facing a basic level problem about direction cosine matrix as I am not an expert in mathmatics. Hope you people will help me.. I am working on inertial navigation system in three coordinate frames : 1. ENU 2. ECEF (XYZ) 3. LLH (Latitude , Longitude , Height) I...

I was doing a signals and systems problem and I think I might be screwing something up with the cosine function because I get cos(a+b) = cos(a)*cos(b) This is how cos(a+b)=Re\left\{ e^{j*(a+b)} \right\} =Re\left\{ e^{j*(a)}*e^{j*(b)} \right\} =cos(a)*cos(b) Can anyone point out my mistake...

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...

Hello, I am attempting a past exam paper in preparation for an upcoming exam. The past exam papers do not come with answers and I'm a little unsure as to whether I'm doing all of the questions correctly and would like some feedback if I'm going wrong somewhere. Any help is greatly appreciated...