Polar Definition and 1000 Threads

$r=5$ and $\theta=\pi/6$$\frac{dy}{dx}=\frac{\frac{dy}{d \theta}}{\frac{dx}{d \theta}}=\frac{\frac{dr}{d \theta}sin(\theta)+rcos(\theta)}{\frac{dr}{d \theta}cos(\theta)-rsin(\theta)}$ $\frac{0*sin(\pi/3)+5cos(\pi/3)}{0*cos(\pi/3)-5sin(\pi/3)}=-\frac{\sqrt{3}}{3}$is that right?

Suppose T=T(r,θ)=G(x,y) How do you prove ∇T(r,θ)=∇G(x,y)? I can think of some arguments in favor of this equality, but I want an actual proof or a very good intuitive argument. My arguments in favor go something like this: -Gradient vectors should be the same because if my directional...

So I'm wondering, should I use Cartesian or Polar Coordinates to store intergalactic objects in DB? I'm currently prototyping a game idea that can be oversimplified as a spaceship simulator in infinite space. I'm considering grouping objects together so that they have a "parent super-space"...

Lim (x, y)->(0,0)(X^3+y^3)/(x^2+y^2) The answer is -1, but I can't get it there. Here is what I did. ((Rcosx)^3 +(rsinx)^3)/((rcosx)^2+(rsinx)^2) Then by factoring out a r squared from top and bottom I'm left with a denominator of (sin^2(x ) + cos^2 (x)) which simplifies to 1. And a numerator...

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...

Hi guys, I'm assuming that CS2 is a nonpolar molecule and Al2S3 is a polar molecule. Would I be correct? Thanks in advance.

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 Find the area of the region that consists of all points that lie within the circle r = 1 but outside the polar equation r = cos(2θ) Homework Equations A = ∫ 1/2 (r2^2 - r1^2) dθ, where r2 is outer curve and r1 is inner curve. The Attempt at a Solution Here is...

Homework Statement Find the area of the region. Interior of: r = 2 - sin(b) Homework Equations A = 1/2 ∫ (r)^2 dr The Attempt at a Solution I really don't have any idea how to approach this problem. I don't understand how to determine my limits of integration. The only part of the problem I...

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...

Homework Statement The graph of the polar curve r=2-cosΘ for 0≤θ≤2pi is shown in the figure. (attached) a) write an integral expression for the area of the region inside the curve b) write expressions for dx/dΘ and dy/dΘ in terms of Θ c) find dy/dx as a function of Θ d) write an equation in...

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...

I'm really stumped here as usual. Here is what I've managed to figure out. I'm given two equations. r=2 r=4cos(theta)I converted them both to rectangular coordinates to get an idea of what the graph would look like. I need to find either the area in red or the area in green. (In this case...

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} Then i plotted points to...

Homework Statement Convert -2+2√3i to polar coordinates. Homework Equations r = √x2+y2 θ = tan-1(y/x) The Attempt at a Solution I am confused because θ = tan-1(2√3/2) = tan-1(√3) = -π/3 and r = 4, so that would make the polar form 4cis(-π/3), but the calculator gives: 4cis(2π/3). I...

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 so i have (2,7pi/3)...

I'd like to understand why i cannot seem to be able to define unit polar basis vectors. Let me explain: We have our usual polar coordinates relation to Cartesian: x = r cosθ ; y = r sinθ if I define \hat{e_{r}}, \hat{e_{\vartheta}} as the polar basis vectors, then they should be...

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...

Kind of just a general question...I took a theoretical physics class last semester and we went through this whole book "Div, Grad, Curl, and All That Vector Calculus". Now I'm in an upper division E&M class and we're using Griffith's "Intro to Electrodynamics". In my 3rd semester of calculus and...

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...

It is known that the vector in polar coordinate system can be expressed as \mathbf{r}=r\hat{r}. In this formula, we don't see \hat{\theta} appear. But after the derivation yielding speed, \mathbf{v}=\dot{r}\hat{r}+r\dot{\theta}\hat{\theta}. Where does theta come from? And how to define its...

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...

Homework Statement So I am not sure how to multiply these two (A*R^2) together. Homework Equations A=( x^2 + y^2 + z^2 ) (xe + y e + z e ) Where x represents the three vector compones I also have R^2=x^2+y^2+z^2 The Attempt at a Solution Is the product of A (x^3e + y^3 e + z^3...

What is the functional form of rose petal with 6 petals? I am asked to graph this function with matlab, but it seems impossible according to my calculus textbook. According to my textbook, a rose curve can have the form r = a \cos n \theta or r = a \sin n \theta. When n is even, then there are...

Homework Statement Find a polar equation for the curve represented by the Cartesian equation. y=1+3x Homework Equations x2+y2=r2 x=Rcos(θ) y=Rsin(θ) The Attempt at a Solution (1+3x)2+x2=r2 1+6x+10x2=r2 1+6rcos(θ)+10r2cos2(Θ)=r2

Homework Statement Find the points at which the following polar equation has horizontal and vertical tangents: r2 = 4cos(2θ)Homework Equations \frac{dy}{dx} = \frac{r'(θ)sinθ + r(θ)cosθ}{r'(θ)cosθ - r(θ)sinθ} Horizontal Tangent: \frac{dy}{dθ} = 0; \frac{dx}{dθ} ≠ 0 Vertical Tangent...

Homework Statement r = 3sin\theta since x= rcos\theta x = 3sin\thetacos\theta and since: y = rsin\theta y = 3sin^2\theta Then I'm sort of stuck..

I'm working on a problem that requires me to take the cartesian metric in 2D [1 0;0 1] and convert (using the transformation equations b/w polar and cartesian coords) it to the polar metric. I have done this without issue using the partial derivatives of the transformation equations and have...

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!

I was trying to study vectorial kinematics in all its fullness, without decorating formulas, only deducting all vectorially through mathematical definitions. I felt much difficulty, because it's a puzzle of many pieces and I not found a embracing explanation in any book. Someone could explain to...

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 ∫^{4}_{0} ∫^{√(4y-y^{2})}_{0} (x2) dx dy The attempt at a solution I'm confused on how to convert the bounds into polar coordinates. I believe x2 just becomes r2cos2θ 0≤x≤√(4y-y2) 0≤y≤4 but i don't know how to convert the bounds

Homework Statement The plane z = 2 and the paraboloid z = 8 − 6x2 − 6y2 enclose a solid. Use polar coordinates to find the volume of this solid. Homework Equations ∫∫R f(x,y) dA = ∫βα∫ba f(rcosθ, rsinθ) r dr dθ The Attempt at a Solution z = 2, z = 8 − 6x2 − 6y2 Setting these two equal, we...

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 I need to find i1+i2 Homework Equations for i1=0.092<-98.86 i2=-4i1-j10/25=-4i1-0.4 i1=0.092<-98.86 x=rcosθ=0.092cos(-98.86)=-0.0142 y=rsinθ=0.092sin(-98.86)=-0.0909 i1=-0.0142-j0.0909 Therefor...

Homework Statement A=1.5495<21.0363°x(22.1009<30.3658°/69.9667<9.1884°) Homework Equations The Attempt at a Solution A=1.5495<21.0363x(22.1009/69.9667(30.3658-9.1884)=1.5495<21.0363(0.3159<21.1774)=(1.5495x0.3159)(21.0363+21.1774)=0.4895<42.2137° Solution above is it correct or I have to...

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 Hi wondering what the directrix is for this Homework Equations r = (20)/ (2+sin(theta)) The Attempt at a Solution I factored denominator so it read 2(1+ (1/2)sin(theta)) ...So I said e times d = (2/20) and I got d = (1/5) because e is (1/2). Doesn't make...

Homework Statement I want to know if I did these right. Write a polar equation of a conic with the focus at the origin and the given data. Homework Equations r = (ed) /(1+- cos(theta)) and r = r = (ed) /(1+- sin(theta)) The Attempt at a Solution Parabola , directrix x = -3 I...

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...