Polar Definition and 1000 Threads

I have a scalar quantity ##V## (let's call it a voltage for concreteness) that is a function of angle ##\theta##. There are two obvious ways to plot it, as a Cartesian plot (see A above) or as a polar plot (see B). I can also express the polar plot in terms of Cartesian coordinates ##V_x = V \...

I am really confused about coordinate transformations right now, specifically, from cartesian to polar coordinates. A vector in cartesian coordinates is given by ##x=x^i \partial_i## with ##\partial_x, \partial_y \in T_p \mathcal{M}## of some manifold ##\mathcal{M}## and and ##x^i## being some...

Why is it when I plot a circle from ##\theta \in [\pi/2,-\pi/2]## I get the right side of the unit circle: PolarPlot[1, {\[Theta], \[Pi]/2, -\[Pi]/2}] ? Shouldn't I get the left side?

Let's take two orthogonal curves in polar coordinates of the form ##\langle r,\theta \rangle##, say ##\langle r,0\rangle## and ##\langle r,\pi/2\rangle##. Cleary both lines are orthogonal, but the dot product is not zero. This must be since I do not have these vectors in the form ##\langle...

Hi PF! I have a function that looks like this $$f(r,\theta) = \sinh (\omega \log (r))\cos(\omega(\theta - \beta))$$ You'll notice ##f## is harmonic and satisfies the BC's ##f_\theta(\theta = \pm \beta) = 0##. Essentially ##f## has no flux into the wall defined at ##\theta = \pm \beta##. So we...

The analysis is based on 29 radar profiles collected between May 2012 and December 2015. The identified region is about 20-km wide. The report acknowledges the results are consistent with with water or water-laden sediments. A brief discussion on the BBC (with no citations) asserted that...

Please see the attached image. To my understanding, there are two ways to graph a trigonometric function. One is in the Cartesian Coordinate Plane where we have the values (x,y). The other is in the Polar Coordinate system where we have the values (r,θ). In regards to the image that I've...

Hi, The main question revolves around the Rhodonea curve AKA rose curve. The polar equation given for the curve is r=cos(k). The parametric equation is = cos(k(theta)) cos (theta), = cos(k(theta)) sin(theta) . Can anyone show me the conversion from the general parametric form to the general...

Homework Statement What is the sum of position vectors of all points on a circle? Don't use Cartesian system. Homework Equations Sum vector $$\vec s = \int_{\theta=0}^{\theta=2{\pi}}\int_{r=0}^{r=R} \, \,\vec P \, dr d\theta$$ where $$\vec P$$ is the position vector. The Attempt at a...

Homework Statement Question attached in attachments Homework Equations Area enclosed by polar graph is ∫0.5r^2 where r is the radius as a function of angle theta The Attempt at a Solution I attempted to use the formula above and I subtracted the area of the inside from the outside but it...

Homework Statement Homework EquationsThe Attempt at a Solution Part C is confusing me. I got the height PQ to be 16/3root6 But I'm lost as to how to find the length SP. The mark scheme has the answer as 8, or (SP/2 = 4 therefore SP = 8) but I still can't figure it out, maybe it's 'cause...

Hi, I am going around in circles, excuse the pun, with phasors, complex exponentials, I&Q and polar form... 1. A cos (ωt+Φ) = Acos(Φ) cos(ωt) - Asin(Φ)sin(ωt) Right hand side is polar form ... left hand side is in cartesian (rectangular) form via a trignometric identity? 2. But then...

Hey people, this question was already asked here [https://www.physicsforums.com/threads/velocity-in-plane-polar-coordinates.795749/], but I just couldn't understand the answer given, so I was wondering if some of you could help me by explaining it again. I don't really get Equation (or...

Homework Statement [/B] a - a fixed non-zero real number r=e^(a*theta), where -pi/2<theta<pi/22. The attempt at a solution r^2=(e^(a*theta))^2 x^2 + y^2 = e^(2*a*theta) ln(x^2 + y^2) = 2*a*theta ln(x^2 + y^2) = 2*a*(pi+arctan(y/x)) Is this OK?

Homework Statement I am trying to solve the axisymmetric diffusion equation for vorticity by Fourier transformation. Homework Equations $$ \frac{\partial \omega}{\partial t} = \nu \Big( \frac{1}{r}\frac{\partial \omega}{\partial r} + \frac{\partial^2 \omega}{\partial r^2} \Big). $$ The...

Homework Statement I have to calculate the partial derivative of an arctan function. I have started to calculate it but I wonder if there is any simpler form, because if the simplest solution is this complex then it would make my further calculation pretty painful... Homework Equations $$\beta...

Homework Statement Is NBr3 a polar or nonpolar molecule, please draw a lewis structure and a perspective drawing. Homework EquationsThe Attempt at a Solution it is polar because of dipoles?

Homework Statement Homework Equations x^2 + y^2 + z^2 = r^2 Conversion equations between the three coordinate systems The Attempt at a Solution I tried to solve this problem using spherical/cylindrical coordinates from the beginning, but that wouldn't work so I started with cartesian...

For the polar equation 1/[√(sinθcosθ)] I found the slope of the graph by using the chain rule and found that dy/dx=−tan(θ) and the concavity d2y/dx2=2(tanθ)^3/2 This is a pretty messy derivative so I checked it with wolfram alpha and both functions are correct (but feel free to check in case...

$\tiny{up(alt) 244.14.4.8}\\$ $\textsf{Describe the given region in polar coordinates}\\$ $\textit{a. Find the region enclosed by the semicircle}$ \begin{align*}\displaystyle x^2+y^2&=2y\\ y &\ge 0\\ \color{red}{r^2}&=\color{red}{2 \, r\sin\theta}\\ \color{red}{r}&=\color{red}{2\sin\theta}...

Since the distances from the origin $\displaystyle \begin{align*} \rho \end{align*}$ are the same, we can say $\displaystyle \begin{align*} \rho = \frac{3\,\alpha}{2} \end{align*}$ and $\displaystyle \begin{align*} \rho = \beta + \pi \end{align*}$, giving $\displaystyle \begin{align*}...

Homework Statement It's not a homework problem itself, but rather a general method that I imagine is similar to homework. For a given elementary complex function in the form of the product, sum or quotient of polynomials, there are conventional methods for converting them to polar form. The...

Homework Statement Evaluate the triple integral y^2z^2dv. Where E is bounded by the paraboloid x=1-y^2-z^2 and the place x=0. Homework Equations x=r^2cos(theta) y=r^2sin(theta) The Attempt at a Solution I understand how to find these three limits, -1 to 1 , -sqrt(1-y^2) to sqrt(1-y^2) , 0 to...

Hi, I had a question I was working on a while back, and whilst I got the correct answer for it, I was told that there was a second solution to it that I missed. Here is the question. ] I worked my answer out to be sqrt(2)(cos(75)+i(sin(75))), however, it appears there is a second solution...

Homework Statement r=1 and r=1+cos(theta), use a double integral to find the area inside the circle r=1 and outside the cardioid r=1+cos(theta) Homework EquationsThe Attempt at a Solution I am confused on the wording and how to set it up. I tried setting it up by setting theta 0 to pi. and r...

Is O3 molecule polar or non-polar? I am confused. If it is molar, could you explain why? Thinking you.

Any point on the plane can be specified with an ##r## and a ##\theta##, where ##\mathbf{r} = r \hat{\mathbf{r}}(\theta)##. From this, my book derives ##\displaystyle \frac{d \mathbf{r}}{dt}## by making the substitution ##\hat{\mathbf{r}}(\theta) = \cos \theta \hat{\mathbf{i}} + \sin \theta...

Homework Statement I tried to answer the following questions is about the curve surface z= f (x, y) = x^2 + y^2 in the xyz space. And the three questions related to each otherA.) Find the tangent plane equation at the point (a, b, a^2+ b^2) in curved surface z . The equation of the...

Homework Statement I'm suppose to convert Sqrt[12x-2x^2] into a polar equation. Homework EquationsThe Attempt at a Solution I went from that equation to r(sin(theta)^2 + 2cos(theta)^2)= 12cos(theta), I really don't know where to go from there.

Hi, I'm getting into general relativity and am learning about tensors and coordinate transformations. My question is, how do you use the metric tensor in polar coordinates to find the distance between two points? Example I want to try is: Point A (1,1) or (sq root(2), 45) Point B (1,0) or...

Hello All, I'm having a problem with my TI89 where it will output correctly if I input an equation of all one type (polar or rectangular), in whatever format I input the equation in. I'm hoping I just somehow messed up the modes when I reset my calculator! For example if I input (1∠2)...

Hey! :o Using polar coordinates I want to calculate $\iint_D \frac{1}{(x^2+y^2)^2}dxdy$, where $D$ is the space that is determined by the inequalities $x+y\geq 1$ and $x^2+y^2\leq 1$. We consider the function $T$ with $(x,y)=T(r,\theta)=(r\cos \theta, r\sin\theta)$. From the inequality...

< Mentor Note -- thread moved from the Homework physics forums to the technical math forums >[/color] Hello.I was reading recently barton's book.I reached the part corresponding to dirac-delta functions in spherical polar coordinates. he let :##(\theta,\phi)=\Omega## such that ##f(\mathbf...

I need explanation of these formulas for polar coordinate system where position of an object is characterized by 2 vectors: r - from the origin to the object, and Φ - perpendicular to r, in the direction of rotation. https://drive.google.com/file/d/0ByKDaNybBn_eakJmS3dUVXVZUDA/view?usp=sharing...

Homework Statement Find the divergence of the function ##\vec{v} = (rcos\theta)\hat{r}+(rsin\theta)\hat{\theta}+(rsin\theta cos\phi)\hat{\phi}## Homework Equations ##\nabla\cdot\vec{v}=\frac{1}{r^2}\frac{\partial}{\partial r}(r^2v_r)+\frac{1}{r sin\theta}\frac{\partial}{\partial...

Hi, on this page: https://en.wikipedia.org/wiki/Laplace_operator#Two_dimensions the Laplacian is given for polar coordinates, however this is only for the second order derivative, also described as \delta f . Can someone point me to how to represent the first-order Laplacian operator in polar...

Homework Statement question : find the value of \iint_D \frac{x}{(x^2 + y^2)}dxdy domain : 0≤x≤1,x2≤y≤x Homework Equations The Attempt at a Solution so here, i tried to draw it first and i got that the domain is region in first quadrant bounded by y=x2 and y=x and i decided to convert...

Homework Statement Convert x3 -y3 = 6xy into polar equation. Homework Equations x=rcosθ y=rsinθ x2 +y2 = r2 The Attempt at a Solution r3cos3θ - r3sin3θ = 6r2sinθcosθ r(cos2θ/sinθ - sin2θ/cosθ) = 6 r(cosθcotθ -sinθtanθ) =6 r = 6/(cosθcotθ - sinθtanθ)

Homework Statement If ## z=x^2+2y^2 ##, find the following partial derivative: \Big(\frac{∂z}{∂\theta}\Big)_x Homework Equations ## x=r cos(\theta), ~y=r sin(\theta),~r^2=x^2+y^2,~\theta=tan^{-1}\frac{y}{x} ## The Attempt at a Solution I've been using Boas for self-study and been working on...

Hi, everyone. I had an example from my book, but I wasn't sure how they got \dfrac{1}{2}cos\theta on step 7? It seems like once they combined the constants, they ended up with just cos2\theta. Although, they have a \dfrac{1}{2} in front. Can someone help me understand where that constant came...

Hey! :o Let $K$ be a circle with center $C=(x_0,y_0)$ and radius $r$. For each point $P=(p_1, p_2)$ outside the circle let $g_P$ be the line that passes through the intersection points of the tangent from $P$ at the circle and the circle. I want to find the equation of the line $g_p$ (polar)...

Hello all, I am trying to find the algebraic representation of the following numbers: \[rcis(90^{\circ}+\theta )\] and \[rcis(90^{\circ}-\theta )\] The answers in the book are: \[-y+ix\] and \[y+ix\] respectively. I don't get it... In the first case, if I take 90 degrees (working with...

Hello all, Given a complex number: \[z=r(cos\theta +isin\theta )\] I wish to find the polar representation of: \[-z,-z\bar{}\] I know that the answer should be: \[rcis(180+\theta )\] and \[rcis(180-\theta )\] but I don't know how to get there. I suspect a trigonometric identity, but I...

How is this done? My textbook only specifies integrating polar graphs with respect to theta.

Hello everyone, I have a complex number problem that i would greatly appreciate some help with. Thanks in advance to anyone offering their time to make a contribution. Q) Write the following in polar form: I have attempted the question (please see my working below) and have been advised that i...

$\textrm{write an equivalent polar equation}$ \begin{align*}\displaystyle x^2+(y-1)^2&=1 \end{align*} $\textrm{expand and rearrange}$ $$x^2+y^2=2y$$ $\textrm{substitute $r^2$ for $x^2+y^2$ and $r \cos(\theta)$ for $y$}$ $\textrm{then}$ $$r^2=2r\cos(\theta)$$ $\textrm{or}$ $$r=2...

$\textrm{write polar to rectangular coordinates}$ $$r=5\sin{2\theta}$$ $\textit{Multiply both sides by $r$}$ $$r^2=5r[\sin{2\theta}] =5\cdot2[r\cos(\theta)r\cos(\theta)]$$ $\textit{then substitute $r^2$ with $x^2+y^2$ and $[r\cos(\theta)r\cos(\theta)$ with $xy$}\\$ $\textit{then}\\$...

Homework Statement Hello! I will be grateful for your help in deciphering the meaning of a paragraph from the book. I honestly don't understand how they got the semi-circle on the xy graph by transferring it from rθ graph. Homework Equations I attach the screen shot from the book. The Attempt...

Hi, I have been wondering if greenhouse gases always need to be polar molecules. Can a gas also absorb energy, and heat up, without being polar?

So I have this PDE: d2T/dr2 + 1/r dT/dr + d2T/dθ2 = 0. How do I implement dT/dr || [r = 0] = 0? Also, what should I do about 1/r? This is actually the first time I am going to attack FDF in polar/cylindrical coordinates. I can finite-difference the base equation fairly decently; I am just...