Cos Definition and 318 Threads

Hi everyone. i think this is my last thread on PF:frown:! because i am too busy,anyway, 4 months ago i posted a thread named it finding cube roots without using calculator and now i want to know if there is a way or method to find sin and cos without using calculator. And thanks to all who...

Homework Statement I have the solution and everything, I'm just confused why they use cos for Fy and sin for Fx ... Homework Equations I've always known Fx=Fcos and Fy=Fsin .. but now I am getting to different problems and it confuses me The Attempt at a Solution I read many posts and answers...

How to express ##\cos 3x## as a polynomial in ##\cos x##?

Is there a way to motivate the sinus and cosinus functions by looking at their Taylor expansion? Or equivalently, is there a way to see that complex numbers adds their angles when multiplied without knowledge of sin and cos?

Homework Statement Cos 2x =√3/2 Find number of solutions .x∈[0,8π] Homework EquationsThe Attempt at a Solution :[/B] drew the graph of cos 2x.It has a periodicity of π and there are two solutions in each period. So 2*8 =16 solutions totally. But my teacher said that we must take [0,16π] as the...

x = 2 − π cos t y = 2t − π sin t −π ≤ t < π I understand how to eliminate parameter using sin^2 + cos^2 = 1. I can't figure out how to deal with the "2t" in the y equation, if you solve for sin(t) and square, you get ((2t-y)/π )^2 which leaves the parameter. Is there a way to get it into the...

I know that ##\sin^2 x + cos^2 x = 1.## Is this mean that ##\sin^2 2x + \cos^2 2x = 1## or ##\sin^2 3x + \cos^2 3x = 1## or ##\sin^2 4x + \cos^2 4x = 1## and so on?

Homework Statement The first problem was " A 50 N crate is pulled up a 5m inclined plan by a worker at constant velocity. If the plane is inclined at an angle of 37degrees to the horizontal and there exists a constant frictional force of 10N between the crate and the surface, what is the force...

Hey Guys. I'm having a bit of a problem with my solving triangles book. I'm finding the book really easy but there's this one thing that I keep getting wrong. Whenever I'm working with degrees with decimal points my answer aways fluctuates slightly from the real answer. I must be doing something...

I'm trying to find a function for x in [0, L] that minimizes this: \int_0^{L} A \phi(x) \frac{ d \phi(x) }{dx} + B cos(\phi(x))\ d\mbox{x} For real (given) positve numbers A and B. with \phi(0) = 0 \phi(x) is an increasing positve function. Can somebody point me in the right direction?

Homework Statement Superposition of two cosine waves with different periods and different amplitudes. Homework Equations This is basically: acos(y*t) + bcos(x*t) The Attempt at a Solution I looked at different trig functions but it seems it is not a standard solution. I've found solutions...

Homework Statement By using chain rule of differentiation, show that: $$ \frac{\mathrm{d} sin\phi }{\mathrm{d} t} = \dot{\phi} cos\phi , \frac{\mathrm{d} cos\phi }{\mathrm{d} t} = -\dot{\phi} sin\phi , $$ Homework EquationsThe Attempt at a Solution I got this right for a homework problem...

Prove that $\cos \dfrac{\pi}{100}$ is irrational.

Starting from FT relation of delta function, I can write the followings: $$ \int_{-\infty}^{\infty} \cos{\alpha x} dx = 0 $$ $$ \int_{-\infty}^{\infty} \sin{\alpha x} dx = 0 $$ The question is how am I supposed to prove those equations, sin and cos are stable oscillating functions.

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)...

Hi, this would be my first post of many in recent times as I have my maths exam soon! I am doing a lot of past papers and I need some help understand some questions. In the triangle XYZ angle Z is a right angle. If XY= 15mm and YZ=8mm, calculate the angle Y, giving your answer in degrees...

Homework Statement The problem is f(x) = sin2πx - (1/πsquare)*sinπx and its given Bn sin (nπx) = f(x) Question is find Bn. Homework Equations Bn = 2/L ∫ (sin2πx - (1/πsquare)*sinπx) * sin(nπx/L) where L is 1 The Attempt at a Solution I did [/B] ∫ sin2πx * sin (nπx) - (1/πsquare)*sin...

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...

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...

I' m trying to solve something as apparently simple like this cos ax/sin pi*x which appears solved in https://archive.org/details/TheoryOfTheFunctionsOfAComplexVariable in the page 157, exercise 9. second part. I'm trying by Fourier series, but by the moment I can't achieve it. Thanks.

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...

Homework Statement Calculate cos\frac{2\pi}{2n+1} + cos\frac{4\pi}{2n+1} + cos\frac{6\pi}{2n+1} + ... + cos\frac{2n\pi}{2n+1} Homework Equations Complex equations, maybe :p The Attempt at a Solution Let's say z^{2n+1} = 1 The sum is equivalent to the sum of the real even...

Are there any complex solutions to cos x = 2?

So I know \cos n \theta + i \sin n \theta = (\cos \theta + i \sin \theta)^n and by applying binomial to the RHS and taking the real part gives you: \cos n \theta = \sum_{k=0}^{\lfloor {n \over 2} \rfloor} C^n_{2k} (\cos^2 \theta - 1)^k \cos^{n - 2k} \theta . I have come across another...

Fourier transform of density matrix of cos(x+y)*cos(x-y) I would like to know whether there exists a solution to the following integral, \frac{1}{\pi} \int\limits_{-\infty}^{\infty} \cos(x+y)^\alpha \cos(x-y)^\alpha e^{2ipy} The above expression is the Fourier transform of the...

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...

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

For a mass on an incline plane, is the downward force mg cos Θ or -mg cos Θ? I'm inclined to state there should be a negative but from my lectures, the negative does not appear to be stipulated. I was wondering if it's was a mistake by the lecturer. mg cos Θ + FN = 0 mg cos Θ = -FN 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...

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...

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..

Can we prove using the definition of limits of sequences that \lim \, \cos(n) diverges ? I mean can we use a contradiction or show that two sub-sequences have a different limit ?

Consider a trig function such as: y = A cos (bx - c) For the phase shift, we would use (-c/b); which aligns with the original function equation and makes sense to me. But in the case of a trig function such as: y = A cos (-bx + c) For the phase shift, we would use (+c/-b); which would...

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...

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 Generally the inverse cosine of any number > 1 Homework Equations cos x = 2 The Attempt at a Solution Obviously by putting this in a calculator, you get an error so the root has to be complex I used the identity (eiθ+e-iθ)/2 = cosθ through a bit of...

:An object explodes into three equal masses. One mass moves East at a velocity of 15.0 m/s. If a second mass moves at a velocity of 10.0 m/s 45.0 South of East, what is the velocity of the third mass? I drew these vectors tip to tail, then used cos law to determine the velocity...

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...

Q. Use the addition formula cos(u+v) = cos(u)cos(v) - sin(u)sin(v) to derive the following identity for the average rate of change of the cosine function: (cos(x + h) - cos x) / h = cos x ((cos h - 1) / h) - sin x ((sin h) / h) A. cos(x+h) = cosxcosh - sinxsinh subtitute this 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...

Homework Statement Hi folks, I am sure this is very simple but there are not enough steps given in this calculation for my simple brain to get from the beginning to the end! σ = ∫ (dσ/dΩ) = ∫ r2sin2θ (no integral limits given) σ = 2∏r2 ∫ (1 - u2) du (integral from -1 to 1) σ = 8∏r2 / 3...

I am given the problem: 100Sin(ωt+30) +20cos(ωt) and the solution is 78.7<38.9degrees How do I convert to phasor form? I know for this calculation I need the following relationship: √2Esin(ωt-∅)=Ee^(-j∅) At first I tried making both sines and then splitting up 100Sin(ωt+30) and...

Can anyone prove me this stament please.

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)

for cos y the critical points are n*pi - 0.5*pi for cos 2x, the critical points should be n/2 * pi - 0.25*pi because if I set y=2x = n*pi - 0.5*pi , I get the eq in red for x. However if I do it graphically, I just get n*pi - 0.25*pi. The question: why algebraically I am constrained to use...