Polar Definition and 1000 Threads

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  1. DrGreg

    I Cartesian and polar terminology

    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 \...
  2. E

    A Vec norm in polar coordinates differs from norm in Cartesian coordinates

    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...
  3. M

    Mathematica Why Does a Polar Plot of a Circle Only Show One Side of the Unit Circle?

    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?
  4. M

    I Simple dot product in polar coordinates

    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...
  5. M

    I Shifting polar functions vertically

    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...
  6. F

    I Liquid water reservoir reported under Mars polar cap

    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...
  7. opus

    B Understanding Polar and Cartesian Graphs: Comparing Two Coordinate Systems

    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...
  8. Alphonso2001

    B Conversion of parametric form to polar for the rose curve

    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...
  9. Kaguro

    Understanding Polar Vectors on a Circle

    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...
  10. C

    Finding area enclosed by the polar curve

    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...
  11. T

    Polar curves/Area of rectangle

    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...
  12. N

    Sinusoids as Phasors, Complex Exp, I&Q and Polar form

    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...
  13. T

    Velocity in polar coordinates (again)

    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...
  14. Poetria

    Polar equation to rectangular equation

    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?
  15. R

    Diffusion equation in polar coordinates

    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...
  16. Robin04

    Divergence of a vector field in a spherical polar coordinate system

    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...
  17. reese houseknecht

    NBr3: Polar or Nonpolar Molecule?

    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?
  18. Phantoful

    How do I define a region in R3 with spherical/polar coords?

    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...
  19. A

    I Why does this concavity function not work for this polar fun

    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...
  20. karush

    MHB 244.14.4.8 Describe the given region in polar coordinates

    $\tiny{up(alt) 244.14.4.8}\\$ $\textsf{Describe the given region in polar coordinates}\\$ $\textit{a. Find the region enclosed by the semicircle}$ \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}...
  21. P

    MHB Harrison's question via Facebook about polar functions

    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*}...
  22. T

    How do you always put a complex function into polar form?

    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...
  23. S

    Triple Integral of y^2z^2 over a Paraboloid: Polar Coordinates Method

    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...
  24. T

    MHB Additional solution for polar form of complex number

    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...
  25. S

    Area Calculation for Circle and Cardioid Using Double Integrals

    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...
  26. I

    Is the O3 Molecule Polar Due to Fractional Charges and Nonlinear Geometry?

    Is O3 molecule polar or non-polar? I am confused. If it is molar, could you explain why? Thinking you.
  27. Mr Davis 97

    Deriving Polar Coordinates Without Cartesian System

    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...
  28. D

    Finding the volume surrounded by a curve using polar coordinate

    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...
  29. Q

    Quick Question about Converting Polar cordinates

    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.
  30. T

    I Finding distance in polar coordinates with metric tensor

    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...
  31. S

    TI89 Not Displaying Polar Correct Coordinates

    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)...
  32. M

    MHB Calculating integral using polar coordinates

    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...
  33. amjad-sh

    Dirac-delta function in spherical polar coordinates

    < Mentor Note -- thread moved from the Homework physics forums to the technical math forums > 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...
  34. M

    Newton's laws in polar coordinates

    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...
  35. karush

    MHB Evaluating Improper Integrals in Polar Coordinates

    15.3.65 Improper integral arise in polar coordinates $\textsf{Improper integral arise in polar coordinates when the radial coordinate r becomes arbitrarily large.}$ $\textsf{Under certain conditions, these integrals are treated in the usual way shown below.}$ \begin{align*}\displaystyle...
  36. T

    The Divergence of a Polar Vector Function

    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...
  37. S

    What is the gradient in polar coordinates?

    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...
  38. D

    Trying to find this double integral using polar coordinates

    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...
  39. S

    Convert x^3 -y^3 = 6xy into polar equation

    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)
  40. rhdinah

    Polar Partial Derivatives - Boas Ch 4 Sect 1 Prob 13

    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...
  41. H

    How Do You Derive the \(\dfrac{1}{2}\cos\theta\) in Step 7?

    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...
  42. M

    MHB How Do You Find the Equation of a Polar Line for a Circle with Given Points?

    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)...
  43. Y

    MHB Complex Numbers - from Polar to Algebraic

    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...
  44. Y

    MHB Polar Representation of a Complex Number

    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...
  45. G

    B How to integrate a polar graph with respect to radius

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

    MHB Complex Numbers - writing in polar form

    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...
  47. karush

    MHB 639.7.6.97 write an equivalent polar equation

    $\textrm{write an equivalent polar equation}$ \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...
  48. karush

    MHB -10.1.1 write polar to rectangular

    $\textrm{write polar to rectangular coordinates}$ $$r=5\sin{2\theta}$$ $\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 $xy$}\\$ $\textit{then}\\$...
  49. Vital

    How is the xy curve formed from the rθ curve?

    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...
  50. M

    Do greenhouse gases need to be polar?

    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?
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