Polar coordinates Definition and 569 Threads

The conic equation has 2 versions in cartesian coordinates: The general: ##Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0## And the parametric: ##y^2 = 2px + (e^2-1)x^2## In polar coordinates, I known just the parametric: ##r = \frac{p}{1+e\cos(\theta)}## But exist a general form too?

Homework Statement Need a free program to plot expressions in polar coordinates. For example, I want to plot the equipotentials for an expression in polar coordinates of the potential for a dipole charge, 4q and -q separated by a distance L. Homework Equations V=kq(4/r1 - 1/r), where r12...

Homework Statement A particle moves with const speed v along the curve r(θ) = a(1+cos θ). Starting with the general expression for the velocity vector v in polar coordinates solve for θ_dot in terms of v, k, and θ. What does the sign of θ_dot signify?Homework Equations v = r_dot*r_hat +...

given that x'=f(x,y) y'=g(x,y) iff the vector function (r, θ) is a sloution of the system r'=f(rcosθ,rsinθ)cosθ +g(rcosθ,rsinθ)sinθ am trying to show that this is true but i just don't get where the sinθ and cosθ come from, how do i get to that

In a problem that requires converting from cartesian to polar coordinates, I need to take \frac{dr}{dx}. I tried doing it two different ways but getting two completely different answers.. Method 1: r=\sqrt{x^2+y^2} \frac{dr}{dx}=\frac{1}{2}\frac{1}{\sqrt{x^2+y^2}}2x \;\; =...

Homework Statement ∫∫Rarctan(y/x) dA, where R={(x,y) | 1\leqx2+y2\leq4, 0\leqy\leqx Homework Equations x=rcos(θ) y=rsin(θ) x2+y2=r2 The Attempt at a Solution I know that the range of r is 1 to 2 but I can't figure out how to change the second part into θ. If I change y and x to...

Dear Math and Physics fans You have always been so helpful in the past and I was hoping that I could call on your expertise once again. I want to make a wedge filter in MATLAB so I can determine the orientation of the ellipse of a centered 2D fft. I tried to make an new image where...

Homework Statement I have a function y that is axisymmetric, so that y=y(r). I want to solve for r such that ∇2y(r) = Z. Can anyone tell me if I'm following the right procedure? I'm not sure since there are two "∂/∂r"s present... Homework Equations ∇2 = (1/r)(∂/∂r)(r*(∂/∂r)) +...

Homework Statement hi,guys. The directions of shooting e=cos\alphacos\varphii+cos\alphasin\varphij+sin\alphak 0<\varphi<=2π;\varphi -horizontally \alpha[0,π];\alpha is vertically initial speed=v0 I need to calculate the surface equation of canon shots (where it hits). In other words equations...

Polar Coordinates --- Graphing the points of when theta<0 Hi everyone, I'm working with an online graphing program desmos.com. It's great, and actually tons of fun. I'm currently working with polar coordinates but the only flaw of this grapher is that when working with polar coordinates...

1. Homework Statement [/b] Suppose the lim(x,y) →(0,0) (xy)/SQRT[x^2 + y^2] if it exists find the limit. The Attempt at a Solution x = rcosΘ y = r sinΘ r = SQRT[x^2 + y^2] ∴ lim[SUB]r → 0 (r2cosΘrsinΘ)/ r = rcosΘsinΘ \leq r and so -r \leq(xy)/SQRT[x^2 + y^2] \leq r ... ... I can...

Give all the polar coordinates corresponding the rectangular point $$(-1, \sqrt{3})$$ Am i setting this up right? so would I use $$(r, \theta)$$ so $$x = rcos(\theta)$$ $$y = rsin(\theta)$$ $$r^2 = x^2 + y^2$$ so: $$(-1)^2 = (-1*\frac{2\pi}{3})^2 + (-1*\frac{11\pi}{6})$$ ?

I don't understand why I am screwing this up so bad. Sketch the graph of the equation $$r = 2 + 4cos(\theta)$$ in polar coordinates. So I did: $$0 = 2 + 4cos(\theta) $$ $$= -\frac{1}{2} = cos(\theta)$$ Then got $$cos(\theta)$$ is $$-\frac{1}{2}$$ @ $$\frac{2\pi}{3}$$ and @$$ \frac{4\pi}{3}...

Plot the point whose polar coordinates are given. Then find two other pairs of polar coordinates of this point, one with r > 0 and one with r < 0 so I did $$\frac{\pi}{3} + 2\pi = \frac{7\pi}{3} \therefore$$ $$r > 0$$ and did $$\frac{\pi}{3} + \pi = - \frac{4}{3} \pi$$ $$\therefore$$ $$r < 0$$...

First, I'd like that you read this littler article (http://mathworld.wolfram.com/NaturalEquation.html). The solution given by Euler that coonects the system cartesian (x, y) with the curvature κ of the "cesaro system" (s, κ), is that the derivative of the cartesian tangential angle φ* wrt arc...

In the wiki, there is an explanation for what is the tangential angle in cartesian and polar coordinates. However, the orientation these angles aren't specified. In cartesian coordinates, I believe that the tangential angle φ is measured from the x-axis, in polar coordinates the tangential angle...

Homework Statement Image attached Homework Equations r2=x2+y2 The Attempt at a Solution ∫∫ re-r^2 drdΘ I'm not sure how to establish the boundaries. This is an online class so if you can offer any additional tips for evaluating types of integrals of this sort, that would be...

I've been watching the Stanford lectures on GR by Leonard Susskind and according to him the metric tensor is not constant in polar coordinates. To me this seems wrong as I thought the metric tensor would be given by: g^{\mu \nu} = \begin{pmatrix} 1 & 0\\ 0 & 0\\ \end{pmatrix} Since...

Hellow! I have searched for some theory about linear system in polar coordinates, unfortunately, I not found anything... exist some theory, some book, anything about this topic for study? Thanks!

Homework Statement ∫∫√(x^2+y^2)dxdy with 0<=y<=1 and -SQRT(y-y^2)<=x<=0 Homework Equations x=rcos(theta) y=rsin(theta) The Attempt at a Solution 0.5<=r=1, we get r=0.5 from -SQRT(y-y^2)<=x by completing the square on the LHS then, 0<=theta<=pi But, when I calculated the...

Homework Statement Use polar coordinates to set up and evaluate the double integral f(x,y) = e-(x2+y2)/2 R: x2+y2≤25, x≥0 The Attempt at a Solution First I just want to make sure I'm understanding this my double integral would be ∫^{\pi/2}_{-\pi/2} because x≥0 ∫^{5}_{0}...

Homework Statement Use polar coordinates to find the volume of the given solid. Enclosed by the hyperboloid -x2 - y2 + z2 = 1 and the plane z = 2 Homework Equations r2 = x2 + y2, x = rcosθ, y = rsinθ ∫∫f(x,y)dA = ∫∫f(rcosθ,rsinθ)rdrdθ The Attempt at a Solution -x2 - y2 + 4...

Homework Statement x = eKcos(k) y=eKsin(k) -∞ < K < ∞ Find an equation in polar coordinates for the above curve The Attempt at a Solution I am not fully clear as to what the question is asking. If its asking for (r,k), where K is normally a theta value then it would be...

Homework Statement Convert ∫ from 0 to 3/√2 ∫ from y to √(9-y^2) of xydxdy to polar form. Homework Equations x2+y2=r2 The Attempt at a Solution I found the equation x2+y^2=9 from the upper range of the second integral. So r=3. Therefore r ranges from 0 to 3. The integrand is...

Homework Statement Convert (1,-2) to polar coordinates find one representation with r >0 and one with r <0. Also 0<= theta <= 2 PI Homework Equations I used tantheta = y /x , and x^2 +y^2 = r^2 The Attempt at a Solution I got (sqrt(5) , arctan(-2)) , (-sqrt(5) , arctan(-2) + pi...

i'm trying to integrate some some function bounded by the x-y domain of x2+y2=6y which is a circle on the x-y plane shifted upward where the outer part of the circle is 6. i'm trying to integrate a double integral.. ∫∫f(x)rdrdθ i don't know how to express my limits of integration for r...

1. Evaluate the double integral ∫∫arctan(y/x) dA by converting to polar coordinates over the Region R= { (x,y) | 1≤x^2+y^2≤4 , 0≤y≤x } My attempt at solving Converting to polar using x=rcosθ and y=rsinθ I get ∫∫arctan(tan(θ))r drdθ I understand that I have to integrate first with respect...

Homework Statement Find the volume of the wedge-shaped region contained in the cylinder x^2+y^2=9 bounded by the plane z=x and below by the xy planeHomework Equations The Attempt at a Solution So it seems a common theme for me I have a hard time finding the limits of integration for the dθ term...

Homework Statement Evalutate the double integral sin(x^2+y^2)dA between the region 1≥x^2+y^2≥49 The Attempt at a Solution so r^2 = x^2 + y^2 dA = rdrdθ so I can turn this into double integral sin(r^2)rdrdθ where the inner integral integrated with respect to dr goes from 1 to 7...

Homework Statement Draw the graph of r = 1/2 + cos(theta) Homework Equations The equation is itself given in the question. It is a Limacon. The Attempt at a Solution Step-1 ---> Max. value of r is 1/2 + 1 = 3/2 [ at cos (0) ] Min. value of r is 1/2 - 1...

Homework Statement Consider a planet orbiting the fixed sun. Take the plane of the planet's orbit to be the xy-plane, with the sun at the origin, and label the planet's position by polar coordinates (r, \theta). (a) Show that the planet's angular momentum has magnitude L = mr^2 \omega, where...

show that \frac{d\hat{r}}{dt}=\hat{θ}\dot{θ} also, \frac{d\hat{θ}}{dt}=-\dot{θ}r i've tried finding the relationship between r and theta via turning it into Cartesian coord.s, and I've tried the S=theta r but still no luck. S=theta r dS/dt=d(theta)/dt r which is similar to the RHS...

\nabla^2 u=\frac {\partial ^2 u}{\partial x^2}+\frac {\partial ^2 u}{\partial y^2}=\frac {\partial ^2 u}{\partial r^2}+\frac{1}{r}\frac {\partial u}{\partial r}+\frac{1}{r^2}\frac {\partial ^2 u}{\partial \theta^2} I want to verify ##u=u(r,\theta)##, not ##u(x,y)## Because for ##u(x,y)##, it...

Homework Statement Consider the function in polar coordinates ψ(r,θ,\phi) = R(r)sinθe^{i\phi} Show by direct calculation that ψ returns sharp values of the magnitude and z-component of the orbital angular momentum for any radial function R(r). What are these sharp values? The Attempt at a...

Homework Statement Find the area inside the circle r = 3sinθ and outside the carotid r = 1 + sinθ The Attempt at a Solution Alright so I graphed it and found that they intersect at ∏/6 and 5∏/6. I can't think of a good way to approach the problem. The carotid has some of it's area...

Homework Statement r=7sin(∅) find the center of the circle in Cartesian coordinates and the radius of the circle The Attempt at a Solution My math teacher is impossible to understand >.< and then the stupid homework is online and crap blah this class but I REALLY want to understand the material...

Homework Statement I have to turn this homework in online... I just want someone to check my work Convert from Cartesian coordinates to Polar coordinates (-1,-sqrt(3)) if r > 0 and if r < 0. Homework Equations The Attempt at a Solution if r > 0 then I believe the answer is...

Homework Statement I don't know how to make theta so ∅ = theta. find the slope of the tangent line at r = sin(6∅) when ∅ = pi/12 Homework Equations y=rsin(6∅) x=rcos(6∅) r=sin(6∅) tangent line equation y-y' = m(x-x') m = dy/dx The Attempt at a Solution when ∅ = pi/12 then...

Homework Statement Hi everybody... i have a bad problem with my brain: starting from the Vectorial form of the magnetic dipole: \vec{B}(\vec{r}) =\frac{\mu_0}{4 \pi} \frac{3 \vec{r} ( \vec{r} \cdot \vec{m}) - r^2 \vec{m}}{r^5} Homework Equations i want to derive the spherical...

Homework Statement Find the shortest distance between two points using polar coordinates, ie, using them as a line element: ds^2 = dr^2 + r^2 dθ^2Homework Equations For an integral I = ∫f Euler-Lagrange Eq must hold df/dθ - d/dr(df/dθ') = 0 The Attempt at a Solution f = ds = √(1 + (r *...

Hi, I have a data set containing values for power and direction. I would like to produce a probability density estimate. The data can have multiple sources so I want to use a nonparametric method. I work in python which has a method for kernal density estimation (KDE), which I think should be...

hi all, attached here is my code for 2d fdtd in polar coordinates, from 'numerical electromagnetic: the fdtd method (umran s inan, pg 94-96) written in fortran90. I have try a few approach I could think about to troubleshoot this code but the output is still infinity. Anybody here can give me...

Homework Statement Use polar coordinates to find the volume of the solid bounded by the paraboloid z = 47 - 5x2 - 5y2 and the plane z = 2. Homework Equations x2 + y2 = r2 x = rcosθ y = rsinθ The Attempt at a Solution I substituted the z = 2 into the equation given, 2 = 47 -...

Find the area of the following region: Inside: r2 = 6 cos 2θ Outside: r = √3 Here's how I've set up the integral. I have to be making a mistake somewhere in the set up, but I can't figure it out. r1 = √3 r2 = (\sqrt{6 cos 2θ}) \frac{Area}{4}= \frac{1}{2}\int\ (\sqrt{6 cos 2θ})^{2}...

I quote a question from Yahoo! Answers I have given a link to the topic there so the OP can see my response.

In polar coordinates we have \vec{r} = r \hat{r} \Rightarrow \vec{v} = \frac{d}{dt}({r \hat{r}}) = \dot{r}\hat{r} + r \frac{d \hat{r}}{dt} . In the book Introduction to Mechanics, K & K says the right term is the component of velocity directed radially outward. (Surely a typo, as the left...

I know that \oint_{C}\mathrm{d}\vec{l} = 0, for any closed curve C. But when i try to calculate the integral around the unit circle in polar coordinates, I get a result different from zero. Here is my approach : \oint_{C}\mathrm{d}\vec{l} = \int_{0}^{2\pi}\hat{\phi}\mathrm{d}\phi =...

Hello =] I'm having trouble with this question, can somebody please help me with it! I'll thanks/like your comment if help me =) ![Question][1] I know that for a ellipse the parametric is x=a sin t , b= b cos t t:0 to 2pi (?) for part a) I drew up the graph but not sure if it's...

Homework Statement Find polar coordinates. Homework Equations Cartesian: (-3,4) The Attempt at a Solution r = sqrt(9+16) = 5 sinθ = 4/5 cosθ = -3/5 θ = ∏ - arctan(4/3) Answer: (5, ∏ - arctan(4/3)) I do not understand why we have subtracted the value arctan(4/3) from pi?

Homework Statement Curve C is given in Polar Coordinates by the equation r=2+3sinθ. Consider the usual Cartesian plane and take O as the pole and the positive x-axis as the polar axis. Find points on the curve C where the tangent lines are horizontal or vertical and sketch the curve C...