Polar Definition and 1000 Threads

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  1. S

    [Not Homework] Polar Equation Problem Involved Tangents

    Not homework, just trying to learn how to solve this problem for an exam. Homework Statement https://dl.dropbox.com/u/23889576/Screenshots/10.png Homework Equations \int_{a}^{b} \sqrt { (\frac{dr}{dθ})^2 + r^2 }\, dθ The Attempt at a Solution Had much difficulty, could not...
  2. S

    Integrating Polar Curves over Period

    Hello. I am having trouble conceptualizing and/or decisively arriving to a conclusion to this question. When finding the area enclosed by a closed polar curve, can't you just integrate over the period over the function, for example: 3 cos (3θ), you would integrate from 0 to 2pi/3? It intuitively...
  3. A

    MHB Best Way to Graph in Polar Coordinates

    what is the best way to graph in polar coordinates say r = 3 - 5 \cos \theta is it to plot several points then make a curve between them or ?
  4. S

    Ellipse and Kepler's Law in Polar Coordinates

    Greetings everyone, I am having difficulties grasping the polar form of the ellipse equation, and there seems to be more than one way to express an ellipse in this form, if I am not mistaken. For example on the following webpage http://farside.ph.utexas.edu/teaching/301/lectures/node155.html...
  5. M

    Integration of a vector field in polar coordinates

    Hello all, I am trying to understand how to integrate a vector field in polar coordinates. I am not looking to calculate flux here, just the sum of all vectors in a continuous region. However, there is something I am not doing properly and I am a bit lost at this point. Any help would be...
  6. C

    Finding polar and cartesian form for this power

    Homework Statement ((-1+i)/(√2))^1002 find polar and cartesian form Homework Equations The Attempt at a Solution So I started by finding |z|=1 and Arg(z)= arctan (-1) = 5pi/6 so 1^(1002)*e^(i*5pi/6)*1002 =1*e^(i*835pi) but that's as far as I got because the answer...
  7. D

    Applying Green's THM, Polar Coords substitution

    Use Green's THM to calculate the line integral ∫C(F<dot> dx), where C is the circle (x-2)2 + (y - 3)2=1 oriented counterclockwise, and F(x,y)=(y+ln(x2+y2), 2tan-1(x/y)). Green's THM ∫∂SF<dot>dx=∫∫S(∂F2/∂x) - ∂F1/∂y) I tried doing it by brute force. I took the partials and put them...
  8. V

    Limits of integration for regions between polar curves

    Alright. I completely confused about determining the area between regions of polar curves. However, I do feel that I have a solid grasp in finding areas for single functions. For a given function in polar form, I know that I find the limits of integration by setting the function equal to zero...
  9. C

    Why Does Arg(z) of a Complex Number Differ in Solutions?

    Homework Statement express the arg(z) and polar form of (1/\sqrt{2}) - (i/\sqrt{2}) Homework Equations The Attempt at a Solution Ok so I did \sqrt{(1/\sqrt{2})^{2}+(1/\sqrt{2})^{2}} = 1 so tan^{-1}(1) = \pi/4 so arg(z)=5\pi/4 but they had the answer as -3\pi/4 Am I...
  10. R

    Use polar coordinates to find the volume of the given solid.

    Homework Statement 1. Use polar coordinates to find the volume of the given solid. 2. Inside the sphere x^2 + y^2 + z^2 = 16 and outside the cylinder x^2 + y^2 = 4. 2. The attempt at a solution My attempt as following: 2<=r<=4, and 0<=theta<=2pi So I do a double integral of...
  11. D

    Determining signs (+/-/0) of derivatives from a polar graph

    Homework Statement Use the polar graph to determine the signs (+,-,0) of each derivative at the point labeled A. Homework Equations dy/dx= dy/dtheta= dx/dtheta= dr/dtheta= The Attempt at a Solution Hi people, I need help with this question. See the picture of the graph...
  12. nomadreid

    Is radius a misnomer in a polar equation?

    Is "radius" a misnomer in a polar equation? Often I see the description of "r" in a polar equation r = r(theta) as being "radius", but "radius" is a length, and here you can have a negative r. Hence "radius" is a misnomer, as far as I can tell. Perhaps it would be better described with some...
  13. T

    Understanding what integrating in polar gives you

    I am not understanding integration with polar coordinates, or at least visualizing what is happening. Here's the integral calculated in Wolfram: http://www.wolframalpha.com/input/?i=integrate+%28r%5E2%28cost%5E2-sint%5E2%29%29r+drdt+t%3D%280%29..%28pi%2F2%29+r%3D%281%29..%282%29+ the...
  14. F

    Polar Coordinates to evaluate integrals

    Homework Statement Use Polar coordinates to evaluate were C denotes the unit circle about a fixed point Z0 in the complex plane The Attempt at a Solution I've only used polar integrals to convert an integral in sin and cos into one in therms of z, find the residues and then use the...
  15. J

    Polar Tangent Lines: Finding Slopes at the Pole

    Homework Statement r=2-3cosθ Find the tangent line at any point, and at the point (2,∏) Find the tangent line(s) at the pole Homework Equations Do I have to use x=rcosθ and y=rsinθ to convert it to rectangular to find slopes? The Attempt at a Solution Is the point 2∏ even a...
  16. T

    Converting a polar equation to an x,y equation

    Homework Statement r=(1/(2+cos(θ))Homework Equations r=sqrt(x^2+y^2) rcosθ=x rsinθ=y The Attempt at a Solution Not sure what first step to take. This problem looks so simple, but I can't seem to get far on paper. Not sure if I should multiply both sides by 2+cos and then multiply both sides...
  17. S

    Finding the volume of the cone using cylindrical polar coordinates?

    The cone centre is the z-axis and has base ρ=1 and height z=1, I'm looking at the lecture notes and it says the limit φ=0 to 2pi, z=0 to 1, ρ=0 to (1-z). Could someone tell me where the (1-z) comes from please? Why is it not 0 to 1?
  18. G

    Find polar coordinates (r, θ) of the point.

    Homework Statement The Cartesian coordinates of a point are given. (3,-5) (i) Find polar coordinates (r, θ) of the point, where r > 0 and 0 ≤ θ < 2π. (ii) Find polar coordinates (r, θ) of the point, where r < 0 and 0 ≤ θ < 2π. Homework Equations r^2=x^2+y^2 tanθ=(y/x) →...
  19. ElijahRockers

    Integrate by changing to polar coordinates.

    EDIT: I found my mistake. Theta goes from 90 to 270, not -90 to 90. Wrong side of the y axis. That changes last integration to -2 instead of 2, making final answer -126. Evaluate the given integral by changing to polar coordinates. \int\int_R 3(x+y) dA where R is the region that lies to the...
  20. K

    Differentiating a polar function

    Homework Statement let z=f(x,y) be a differentiable function. If we change to polar coordinates, we make the substitution x=rcos(θ), y=rsin(θ), x^2+y^2=r^2 and tan(θ) = y/x. a. Find expressions ∂z/∂r and ∂z/∂θ involving ∂z/∂x and ∂z/∂y. b. Show that (∂z/∂x)^2 + (∂z/∂y)^2 = (∂z/∂r)^2 +...
  21. M

    Polar coordinates and multivariable integrals.

    Homework Statement Im righting this down for my roommates since he's having tons of trouble trying to figure this out and I can't answer it. also sorry for having to hotlink it. http://i.imgur.com/afShz.jpg the equation is on the image since its very difficult to type it all out...
  22. T

    Nonsensical (lack of) relation between area and arc-length of polar curves

    It is known that the area of a sector of a polar curve is \frac{1}{2}\int r^{2} d \theta This of course comes from the method of finding the area of an arc geometrically, by multiplying the area of the circle by the fraction we want \frac{\theta}{2\pi}\pi r^{2} Today I learned how...
  23. S

    To calculate the polar moment of inertia of a fan

    1.The motors driving the fans of a large cooling tower must be represented in a dynamic simulation of a power plant auxiliary system. Each fan can be described as follows: Fan diameter = 4.5 meter No of blades/fan = 6 Fan RPM = 90 The fan blades have a tapering cross section. The fan...
  24. J

    Kepler's First law Polar to Cartesian

    Forgive me if this is in the wrong thread I'm new here. I am trying to plot an orbit in MatLab using Kepler's First law of motion. In polar form it works fine r(θ) = h^2/μ*(1/(1+e*cos(θ))) h = angular momentum μ = standard gravitational constant and e = eccentricity. The problem is I'd...
  25. D

    Integral calculus: plane areas in polar coordinates

    what is the area inside the graph of r=2sinθ and outside the graph of r=sinθ+cosθ? so i compute for the values of 'r',... but, i only got one intersection point which is (45°, 1.41). there must be two intersection points right? but I've only got one. what shall i do? i cannot compute for...
  26. S

    Sulfuric Acid - Ionic, Polar Molecular or Non Polar Molecular

    What type of bond is Sulfuric Acid (H2SO4(aq))? People tell me its ionic because the acid is made up of a polyatomic ion. However, many sources online say that the acid is polar. I can't seem to figure out which bond it is.
  27. T

    Solving Limit Using Polar Coordinates

    Staff was trying to understand a matter of calculation. I hope someone can explain me in detail how to solve this limit using polar coordinates: http://img36.imageshack.us/img36/2667/semttulokej.png
  28. ElijahRockers

    What are the steps for drawing vectors in polar coordinates?

    Homework Statement Let \hat r = <x_r , y_r> and \hat\theta = <x_\theta , y_\theta> Draw these vectors at points (x,y) = (1,0), (2,0), (3,0), (1,1), (0,1), (0,2). Here is the entire http://www.math.tamu.edu/~vargo/courses/251/HW5.pdf assignment so you can see what context it is in...
  29. B

    Converting polar to cartesian coordinates

    Homework Statement Homework Equations The Attempt at a Solution Do you see that 2 between A and the integral? There's no 2 in the above equation. I don't see where that 2 came from. Everything else is fine.
  30. A

    Transforming from polar to parametric functions

    Hi all, I want to convert a curve from polar coordinates function to a parametric function. The function is: r = 2 \cdot \cos( 4\cdot\theta ) I want to convert this for ( x(t), Y(t) ). Why do I want this? Because I saw that wxMaxima make plots of parametric functions, but I don't know...
  31. Physics Monkey

    Avoiding the Polar Catastrophe in Polar Crystals

    Hi all, As you may know, the interface of LaAlO3 and SrTi03 has received a lot of attention because of the presence of conducting electrons, superconductivity, and ferromagnetism. Because LaAl03 is a polar crystal, the polar catastrophe is often used as a first explanation for the presence of...
  32. F

    Differntial equations & Polar Coords

    Let Q = theta Let z=reiQ z' = (a+ib)reiQ - z|z|2 |z|2 = r so z' = a*reiQ + ib*reiQ - r2eiQ Also z' = ireiQ The question asks for 2 differential equations, but I really have no idea where I'm going with this.. Any help? Thanks
  33. J

    X and y components of polar unit vectors.

    Homework Statement What are the x- and y-components of the polar unit vectors \hat{r} and \hat{\theta} when a. \theta = 180° b. \theta = 45° c. \theta = 215° Homework Equations The Attempt at a Solution Please check if I'm correct, i'll just show my answer for a since the process is...
  34. B

    How Do You Convert Foucault Pendulum Equations to Polar Coordinates?

    Homework Statement For a Foucalt Pendulum: Relative to horizontal Cartesian x and y axes fixed to the Earth (with x as East) the equations of motion for horizontal motion are: x′′ + ω02x -2ωy′ = 0 and y′′ + ω02y + 2ωx′ = 0 [where x′, x′′, y′, y′′ are first and second time...
  35. N

    Polar coordinates of an electric field

    Homework Statement Three charges are arranged as presented below. Q1= 5.00E-9C, Q2= 6.00E-9C and Q3= -7.00E-9C. http://img15.imageshack.us/img15/9250/physicskf.png D) Find the direction of the above electric field using the polar coordinate system 0°< θ <360° Homework Equations...
  36. A

    Area of Polar Curve: Find r = 1 + 2cos(θ)

    Homework Statement Find the area inside the inner loop of the limacon curve : r = 1 + 2cos(θ) Homework Equations A = ∫\stackrel{α}{β}(\frac{1}{2}r2)dθ The Attempt at a Solution i have the solution, my question is : how do you find α and β ? here α = 2π/3 and β = π A =...
  37. ArcanaNoir

    Set up polar area integral of ellipse

    Homework Statement Set up the integral for the area of the ellipse: \frac{x^2}{a^2} =\frac{y^2}{b^2} \le 1 in polar coordinates. Homework Equations maybe \int_\alpha^\beta \int_a^b f(rcos\theta , rsin \theta ) r \; dr \; d\theta or more likely \int_a^b \frac{1}{2} r^2 \; d\theta The...
  38. A

    Unit Vector polar in terms of cartesian

    Homework Statement Prove that the unit vector r{hat} of two-dimensional polar coordinates is equal to r{hat}= x{hat}cosθ + y{hat}sinθ and find the corresponding expression for θ{hat}. all I need is the last part... I'm just not sure what θ{hat} is? How do I go about doing this? Nothing in my...
  39. B

    Cauchy-Riemann Conditions in Polar Coordinates

    Homework Statement Using f(z) = f(re^iθ) = R(r,θ)e^iΩ(r,θ), show that the Cauchy-Riemann conditions in polar coordinates become ∂R/∂r = (R/r)∂Ω/∂θ Homework Equations Cauchy-Riemann in polar coordinates Hint: Set up the derivative first with dz radial and then with dz tangential...
  40. A

    How Does Polar Coordinate Transformation Affect Geometric Figures?

    Hi guys, I'm trying to visualize what polar-coordinate-transform does to geometric figures in cartesian coordinates. It should be a function ℝ2→ℝ2, with domain R2-{0} and range r>0 and -\pi<θ≤\pi. I saw in Needham's Visual Complex Analysis a nice way to visualize such functions: he divides...
  41. I

    Complex Analysis: Using polar form to show arg(z1) - arg(z2) = 2n*pi

    Homework Statement Given that z_{1}z_{2} ≠ 0, use the polar form to prove that Re(z_{1}\bar{z}_{2}) = norm (z_{1}) * norm (z_{2}) \Leftrightarrow θ_{1} - θ_{2} = 2n∏, where n is an integer, θ_{1} = arg(z_{1}), and θ_{2} = arg(z_{2}). Also, \bar{z}_{2} is the conjugate of z_{2}. Homework...
  42. C

    Extract the angle polar numbers

    hi can anybody advise on this, need to find the angle out of the following 2300=2000+(0.5<x).(4<90) got as far as 300/4<90 = 0.5<x = 75<90= 0.5<x is this correct and anybody able to finish this off regards
  43. J

    Ball thrown across a carousel - fictitious forces in polar coordinates

    Homework Statement a carousel is spinning with a constant angular velocity ω. two people, A and B are standing across each other (with the center between them) at distance 2d (d is the radius of the carousel). A throws a ball to B, so B catches it after T seconds. describe the equations...
  44. J

    Converting cartesian surface integral to polar

    If I have an integral: \int\int_{R} x^{2} + y^{2} dy dx Where the region R is the area enclosed by a circle centered on the origin of any given radius, is it possible to just convert x^2 + y^2 to r^2 and integrate from 0 to r over dr and 0 to 2 pi over d\theta? So it would become...
  45. A

    Describe chemical compounds as CHARGED, POLAR or NONPOLAR

    Ok, I thought the only two options in existence were Polar and Non-polar... and I'm being asked which ones are CHARGED? What does this mean? Example: NH4+ (ammonium), NO3- (nitrate), N2, O2, H2O Thanks!
  46. P

    Convert from polar to rectangular

    Homework Statement Convert the polar equation: r = \frac{2}{ 2\,\sin \left( \theta \right) -3\,\cos \left( \theta \right)} to rectangular form Homework Equations x^2 + y^2 = r^2 x = r * cos(theta) y = r * sin(theta)The Attempt at a Solution I tried to to use the x = r cos(theta)...
  47. K

    Converting rectangular to polar

    Homework Statement How do you convert the rectangular coordinate points (1, -2) to polar form? note: rectangular is (x,y) polar is (r, theta)Homework Equations r^2 = x^2 + y^2 , x = rcos(theta) , y = rsin(theta) , tan(theta) = y/xThe Attempt at a Solution So basically, I tried getting it to...
  48. T

    Convert the double integral to polar coordinates

    Homework Statement Evaluate the double integral by converting to polar coordinates. ∫∫ arctan y/x dA; R is the sector in the first quadrant between the circles 1/4= x^2+y^2 and x^2+y^2=1 and the lines y=x/√3 and y=x. Homework Equations arctan y/x= θ The Attempt at a Solution...
  49. G

    United States Calculus 2 - Calculus in Polar Coordinates

    Homework Statement Find the slope of the line tangent to the polar curve at the given point. At the point where the curve intersects the origin, find the equation of the tangent line in polar coordinates. r = 6 sinθ; (-3 7∏/6) Homework Equations The Attempt at a Solution...
  50. I

    Surface integral problem - don't need to use Jacobian for polar?

    Homework Statement Evaluate the surface integral. ∫∫S x^2*z^2 dS S is the part of the cone z^2 = x^2 + y^2 that lies between the planes z = 1 and z = 3. Homework Equations \int \int _{S}F dS = \int \int _D F(r(u,v))|r_u\times r_v|dA x=rcos(\theta) y=rsin(\theta) The Attempt...
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