What is Polar: Definition and 1000 Discussions

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  1. S

    Finding the shared area of 2 polar equations

    Homework Statement Given the two polar equations r=5-3cos(θ) and r=5-2sin(θ) find the area of the region common to both curves. Homework Equations A= 1/2∫ r^2 dθ The Attempt at a Solution i understand that i plug in the two equations into the equation, but i don't know how to find the...
  2. Q

    Integral with Polar Coordinates: Teta Angle Interval

    i just need to know something about the integral with polar coordinates , to know the interval of the teta angle of any domain the proffesor said that we put the pen on the x-axis and move it , i for one moment was not focusing and the doctor had to go to another class can anyone explain ? thank you
  3. N

    Double Integral Polar Coordinates to find area of region

    I'm studying for my final and tutors/my professor isn't available over the weekend. Could someone please spend a little time to help me? My problem is stated as: Let R be the right half of the circle x2+(y-1)2=1. Use a double integral polar coordinates to find the area of the region R. I...
  4. T

    Average Value and Area in Polar

    Homework Statement Let Q be the region bounded by r=sin(3θ) in the first quadrant. Find the area of Q. Find the average distance of points in Q from the origin. The Attempt at a Solution I thought I could calculate area like so: \int_0 ^{pi/3} \int_0 ^{sin(3θ)} sin(3θ) dr dθ This gives...
  5. A

    Transformation from Cartesian to spherical polar coordinates

    Transformation from Cartesian to spherical polar coordinates In dimensions: x=r sinθ cos \varphi and y= r sin θ sin \varphi z=r cos θ Show one example of: ∂z\alpha/ ∂xμ . ∂xμ/ ∂z\alpha = δ\alpha\beta Now here is my answer: δyx=(∂y/∂r . ∂r/∂x) + (∂y/∂θ . ∂θ/∂x) + (∂y/∂\varphi...
  6. I

    Form an op w/ three vectors in polar form.

    Homework Statement I'm trying to find the best solution for solving a problem in which I must form an operation with three vectors in polar form, ending with a sum in rectangular form. The operation is as follows: (5 \angle 0°) + (20 \angle -90°) - (6 \angle180°) = Homework Equations...
  7. M

    Is hydrogen sulphide a polar compound?

    I wanted to know whether H2S is a polar compound and hence does it have a dp dp interaction. An answer sheet says the H2S only has id-id. If this is true can some one explain it to me? cause sulphur is definitively polar, and considering h2s's V shape, it should be a polar molecule, thus having...
  8. T

    Polar Coordinates and Conservative Vector Fields

    Homework Statement Let F = <-y/(x2+y2, x/(x2+y2>. Recall that F was not conservative on R2 - (0,0). In this problem, we show that F is conservative on R2 minus the non-positive x-axis. Let D be all of R2 except points of the form (-x,0), where x≥0. a) If (x,y) is included on D, show that...
  9. S

    Having trouble with double integrals in polar coordinates?

    I'm having trouble figuring out how to find what "r" is. I know r is the radius, but how do I go about finding it? Like what do I look for in a particular problem?
  10. G

    Polar Coordinates Problem

    Homework Statement "Consider the graph of r = e^{\theta} in polar coordinates. Then consider the graph of (\theta \cos{\theta}, \theta \sin{\theta}) where \theta \in \mathbb{R} on the Cartesian plane (x - y axis). How are the two graphs related? What relationship (if any) can we define between...
  11. D

    Polar Integration Domain part 3

    Homework Statement f(x,y) = (x^{2} + y^{2})^-2 x^{2} + y^{2} ≤ 2 x ≥ 1 Homework Equations The Attempt at a Solution -4\pi ≤ θ ≤ 4\pi secθ ≤ r ≤\sqrt{2} are these the correct domain?
  12. D

    Polar coordinate to compute the volume

    Homework Statement Use polar coordinates to compute the volume of the region defined by 4 - x^{2} - y^{2} ≤ z ≤ 10 - 4x^{2} - 4y^{2} Homework Equations The Attempt at a Solution I got z = 2 so set up the equation V = f^{2pi}_{0}f^{5/2}_{2}f^{0}_{2}r*dzdrdθ is the domain...
  13. D

    Domain for Polar Coordinate Part 2

    Homework Statement f(x,y) = e^{x^2+y^2} x^{2} + y^{2} ≤ R Homework Equations The Attempt at a Solution I believe this is a circle. f^{2pi}_{0}^{sqrt(R)}_{-sqrt(R)}e^{x^2+y^2}*r*dr*dθ = f^{2pi}_{0}f^{sqrt(R)}_{-sqrt(R)}e^{r^2}*r*dr*dθ after u substitution... =...
  14. D

    Defining the Domain for a Polar Coordinate Function

    Homework Statement f(x,y) = y(x^{2} + y^{2})^-1 y ≥ \frac{1}{2}, x^{2} + y^{2} ≤ 1Homework Equations The Attempt at a Solution Would you check my domain please? f^{pi}_{0}f^{sqrt(3)/2}_{-sqrt(3)/2} sinθ drdθ
  15. D

    Integration in Polar - polar coordinate

    Homework Statement f(x,y) = xy x ≥ 0, y ≥ 0, x^{2} + y^{2} ≤ 4 Homework Equations The Attempt at a Solution f^{pi/2}_{0}f^{2secθ}_{0} rcosθ * rsinθ * r drdθ I just wanted to check... is this right?? because I really don't think it is
  16. QuarkCharmer

    Arclength of polar cardiod problem

    Homework Statement My textbook sets up the integral, but does not solve, claiming that it's "trivial to solve manually or by using a CAS". I put the integral into my TI-89, and sure enough, there is a solution, and that solution happens to be "8". However... Homework Equations The actual...
  17. K

    Spiral path in polar coordinates problem

    A bee goes from its hive in a spiral path given in plane polar coordinates by r = b*ekt , θ = ct, where b, k, c are positive constants. Show that the angle between the velocity vector and the acceleration vector remains constant as the bee moves outward. (Hint: Find v · a/va.) attempts...
  18. D

    Double Integral problem What am I suppose to do? Related to polar coordinates.

    The problem and my work is shown in the image below. However, I feel like I did something horrible wrong but I'm not sure where! I'm sorry if my handwriting is illegible. If you're having difficulties please leave a comment and I will not hesitate to type it out as a response. Any...
  19. D

    Double Integral, where did I go wrong? Related to polar coordinates.

    ∫∫cos(x^2 + y^2)dA, where R is the region that lies above the x-axis within the circle x^2 + y^2 = 9. Answer: .5pi*sin(9) My Work: ∫(0 ->pi) ∫(0 -> 9) cos(r^2) rdrdθ u = r^2 du = 2rdr dr = du/2r .5∫(0 ->pi) ∫(0 -> 9) cos(u) dudθ .5∫(0 ->pi) sin(u)(0 -> 9) dθ .5∫(0 ->pi)...
  20. R

    How to convert velocity potential from polar form to Cartesian coordinate form

    Homework Statement Alright, here's the question, A stream function for a plane, irrotational, polar-coordinate flow is ψ=9r^2sin^θ. Find out the velocity potential in Cartesian Co-ordinate! Homework Equations The Attempt at a Solution Well, I can easily find out the velocity...
  21. L

    What is the order of polarity for these three molecules on the TLC plate?

    Homework Statement I'm trying to assign the spots for a TLC plate that I did in lab. http://imageshack.us/f/27/tlcpolar.png/ What is the order of polarity of these three molecules? Homework Equations The more polar something is, the lower it will stay on a TLC plate. The less...
  22. B

    Selecting the correct bounds for polar integrals

    Hi! Here's a question I am working on: Double integral of arctan(y/x). where R: 1≤x2+y2≤4, 0≤y≤x. I have the bounds for r as 1 to 2, but for θ I don't know if I should use ∏/4 to ∏/2 or 0 to ∏/2. How do I know which one? The integration is easy, but I need help with the bounds...
  23. T

    Polar Coordinates Improper Integral Proofs

    Homework Statement (a) we define the improper integral (over the entire plane R2) I=\int\int_{R^2}e^{-(x^2+y^2)}dA=\int_{-\infty}^{\infty}\int_{-\infty}^{\infty}e^{-(x^2+y^2)}dy dx=\lim_{a\rightarrow\infty}\int\int_{D_{a}} e^{-(x^2+y^2)} dA where Da is the disk with radius a and center the...
  24. X

    Cartesian and Polar coordinate system increments

    we know that for any (x, y) in Cartesian system, there is such (r, θ) in Polar system, so x = r * cosθ and y = r * sinθ how you can calculate what corresponds to (Δx, Δy) in polar system? how come Δx * Δy = r * Δr * Δθ? Maybe this is very stupid question and has obvious answer...
  25. E

    Easy Polar Coordinates question (Change of variables)

    I have a question regarding problem solving tips. When given an iterated integral and asked to convert it to polar coordinates, how do you select the bounds of theta - do you have to understand how the graph of r operates and therefore know where the theta bounds are based on the rectangular...
  26. J

    Points of Intersection in Polar Areas

    Homework Statement The question is to find the area of the region that lies inside both curves. The part I'm specifically having trouble with is finding the points of intersection. Homework Equations sin (2∅) cos (2∅) The Attempt at a Solution sin 2∅ = cos 2∅ 2 sin ∅ cos ∅ =...
  27. J

    It says convert (-1, pi/8 ) from polar to rectangular coordinate?

    How do you find these on the unit circle: 5pi/2 ? howabout pi/8 ? Converting from polar to rectangular? It says convert (-1, pi/8 ) from polar to rectangular coordinate? But there is no pi/8 on the unit circle? If the'yre on the unit circle just use x=rcosθ and y=rcosθ another example is for...
  28. D

    Particle moving in polar coordinates

    Equations given: r=A\theta \theta=\frac{1}{2}\alphat^{2} A=\frac{1}{\pi} meters per radian \alpha is a given constant Asks to show that radial acceleration is zero when \theta=\frac{1}{\sqrt{2}} radians. I have tried rearranging, plugging in, and deriving to try to solve this...
  29. R

    The tangent to an ellipse from polar coordinates

    I have an ellipse. Quite simple, ecc=0.60. And I'm doodling with calculus I learned 40 years ago. I can find the tangent to the ellipse, that is, the slope of the tangent, using cartestian coordinates. At the point where the tangent skims the top of the minor axis (b) the slope is 0 and and...
  30. C

    Polar compounds that are insoluble in water

    I'm a bit confused about how polar molecules can be insoluble in water. Polar means they have a permanent dipole so I would have assumed that they would solvate water. An example of a polar insoluble compound is pyrantel embonate. Its used to treat hookworm and pinworm infections in the GI...
  31. I

    Polar Coordinates for Point (-5, 3√7) | Solving Using Pythagorean Theorem

    1. Homework Statement A point has coordinates (−5, 3*square root of 7). What is the polar coordinates of this point? (in the form a,b) 2. Homework Equations x= rcos theta y=rsin theta 3. The Attempt at a Solution Using phythagoras thrown -5=x=rcos theta (eq 1)...
  32. C

    Arfken, parity operation on a point in polar coordinates

    Homework Statement Show that the parity operation (reflection through the origin) on a point (\rho, \varphi, z) relative to fixed (x, y, z) axes consists of the transformation: \rho \to \rho \varphi \to \varphi \pm \pi z \to -z Also, show that the unit vectors of the cylindrical polar...
  33. H

    Polar Coordinates Homework: Find the Polar Form of an Expression

    Homework Statement Hi, I have the coordinates of an "expression" for a point in a cartesian coordinate system. I'm trying to write it in a polar coordiante system (in function of r and theta) but I don't know how to find the answer a = y-component of the point b = x-component of the point...
  34. G

    Calculus II - Calculus in Polar Coordinates

    Homework Statement Find the points at which the following polar curves have a horizontal and vertical tangent line. (a) r = 3 + 6 cos(theta) Homework Equations The Attempt at a Solution x = r cos(theta) = (3 + 6 cos(theta)))cos(theta) = 3cos(theta) + 6 cos(theta)^2 y =...
  35. A

    Unit vector in polar coorindate

    In rectangular corr. 3i+j mean leght in x-direction =3 in y-3direction =1 However, how about in polar coorindate? 3r+1\theta (r and \theta are the unit verctor in polar coor., I don't know how to type it out, I hope you understand.) Dose it mean a line with length 3 from origin and angle...
  36. P

    The Mystery of CMB Polar Anisotropy and its Implications on Cosmology

    Hello, friends. I read that polar anisotropy of the CMB shows that the solar sistem is moving towards the Virgin constellation. This polar anisotropy is not something which is not going to cause some problems... First question: Isn't this a sort of ABSOLUTE MOTION? i.e. we have found out...
  37. F

    Use polar coordinates to find the limit

    Hi! Is there somebody, who can help me with this exercise: "Use polar coordinates to find the limit. [If (r, θ ) are polar coordinates of the point (x,y) with r ≥ 0, note that r --> 0+ as (x,y) --> (0,0)]
  38. S

    Areas and Lengths in Polar Coordinates. Calculus 3

    Homework Statement "Find the area of the region that lies inside both curves (as an example), r=((sqrt(3)) cos(theta)) , r=sin(theta). This is Calculus 3. Areas and lengths in polar coordinates. Homework Equations Guys, I'm very confused because when the polar graphs are complicated we...
  39. A

    Polar bear family's noise seal feast

    This unique 6-minute video shows a she-bear and her two cubs devouring a seal, while mummy bear is growling for miles around to be heard, to warn off others from getting too close. http://www.dagbladet.no/2011/09/07/nyheter/innenriks/isbjorn/dyrenes_nyheter/17989869/
  40. A

    How can I integrate an acceleration vector in polar coordinates?

    Hi, Say I have an acceleration vector in polar coordinates: a = -30e_r where the unit vector e_r points in the same direction as the Cartesian unit vector j. How can I integrate that vector so that I have the velocity vector in polar coordinates? I know that if I have an acceleration vector...
  41. A

    Polar Coordinate Tracking problem

    Homework Statement You're tracking a plane from the ground. The plane is at a constant height h from the ground, at a distance r from you at the illustrated instant, and at an inclination theta. The plane's speed is constant at 1200km/hr. Find the rate at which your tracking dish must rotate...
  42. H

    Polar Coordinates: Find dy/dx Problem Solution

    Homework Statement Find dy/dx Problem in picture below Homework Equations The Attempt at a Solution [PLAIN]http://img28.imageshack.us/img28/7162/76013837.png The answer for this is dy/dx = -cos\theta sin\theta + (1-sin\theta)cos\theta/-cos^2\theta - (1-sin/theta)sin\theta I cannot figure...
  43. A

    Polar bear as cartographer's apprentice?

    Or, at least, this young male suddenly appeared on board the cartographer ship "Hydrograf" 2AM. As can be seen on the video, it was very interested in the blue garbage container, and on one of the photos, it has smelled the humans observing it through a ventilation hatch to the (locked) cabin...
  44. D

    Complex operator in polar coords

    Homework Statement If z=x + iy, what is d/dz in polar coordinates? The Attempt at a Solution I know that expanded, d/dz = 1/2 (d/dx) - i (d/dy) Where to go from there?
  45. B

    Converting from polar to rectancular and back again using a TI Voyage 200

    can someone point me to a howto on doing this?
  46. I

    Divergence in spherical polar coordinates

    I took the divergence of the function 1/r2\widehat{r} in spherical coordinate system and immediately got the answer as zero, but when I do it in cartesian coordiantes I get the answer as 5/r3. for \widehat{r} I used (xi+yj+zk)/(x2+y2+z2)1/2 what am i missing?
  47. 2

    Curl in spherical polar coordinates

    Hey, I've been stuck on this question for quite a while now: Homework Statement 1a. Write down an expression for the position vector r in spherical polar coordinates. 1b. Show that for any function g(r) of r only, where r = |r|, the result \nabla x [g(r)r] = 0 is true. Why does this...
  48. X

    Polar coordinates, maximum distance.

    Homework Statement The diagram (omitted) shows the curve C with polar equation r=e^(\theta), where 0\le\theta\le(pi/2). Find the maximum distance of a point of C from the line \theta=(pi/2), giving the answer in exact form. The Attempt at a Solution I'm not really sure how to attack...
  49. A

    Relocate Polar Bears: Antarctic Solution

    After doing lots of research, (about 5 mins) i propose that we relocate polar bears to the antarctic. Plenty of food and plenty of ice. Job done.
  50. A

    Polar bear attacks tourists, one dead, four injured

    http://www.guardian.co.uk/world/2011/aug/05/polar-bear-mauls-british-death Close to Longyear Town on Svalbard, a group of tourists was attacked by an irate polar bear Personally, I would never walk there on my own, but only accompanied by knowledgeable local guides who know the body language of...
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