Polar coordinates Definition and 569 Threads

Homework Statement the circle travels clockwise from (0,-1) to (0,1) write down the parameterization in term of tHomework Equations The Attempt at a Solution x=cost(t) y=-sin(t) i'm not sure about the sign of the polar coordinate, how to find the sign?

Hi, So, I was doing my physics summer work and had no idea what the following question was talking about: Homework Statement For the following polar coordinate points: (4, 0) (4, 60) (4, 90) (4, 135) (4, 180) (4, 270) Describe the locus of points for which a) r = 4 b) r = a...

Homework Statement Find the area of the region inside: r = 9 sinθ but outside: r = 1 Homework Equations The Attempt at a Solution r = 9 sinθ is a circle with center at (0, 4/2) and radius 4/2 while r= 1 is a circle with center at (0, 0) and radius 1. The two curves intersect...

Homework Statement Show that the function f(x,y)= xy/sqrt(x^2+y^2) is continuous at the origin using polar coordinates. f(x,y)=0 if (x,y)=(0,0) Homework Equations r=sqrt(x^2+y^2) x=rcos(theta) y=rsin(theta) The Attempt at a Solution So, converting this equation to polar...

Homework Statement Compute the volume of the indicated solid Below z = sqrt(x^2+y^2), above z = 0, and inside x^2 + (y-1)^2 = 1Homework Equations The Attempt at a Solution My professor solved this in class but I didn't understand why deta is from -pi/2 to pi/2. It is obvious that the...

Homework Statement Hi, I would like to know what is the right way to write continuous deltas standing in a circle of radius a? Homework Equations The Attempt at a Solution I am not sure weather it's δ(r-a) or is it δ(r-a)/|r-a| Thank you

Homework Statement I was looking at the book's example. The author left the final integration as an exercise, and I was attempting it. 1/2 integral of [ (2 - 2sin(delta) )^2 - 0 ] d delta from 0 to 2pi for the sake of work, i will let x = delta (2-2sin(x))^2 => 4 - 8sinx + 4sin^2(x) and i...

Homework Statement evaluate the iterated integral by converting to polar coordinates integral, integral x2dxdy, the limits are 4 to 0 for the outer integral, and /sqrt(4y-y2) to 0 for the inner integral. Homework Equations The Attempt at a Solution well...

Homework Statement Convert to an equation in polar coordinates y = x^(2) Homework Equations x = r cos (theta) , y = r sin (theta) , tan (theta) = y/x The Attempt at a Solution Here is my work so far: y=x^(2) so r sin (theta) = (r cos (theta))^2 and r sin (theta) = r^(2)...

why no change of variable to polar coordinates inside multi-loop integral ?? given a mul,ti-loop integral \int d^{4}k_{1} \int d^{4}k_{2}....\int d^{4}k_{n}f(k_{1} , k_{2},...,k_{n}) which can be considered a 4n integral for integer n , my question is why can just this be evaluated by...

I'm doing work on polar coordinates in double integrals. Could someone explain why when circles aren't centered on the origin the angle only varies from (if it is translated above the origin) 0 to pi. I thought the angle was supposed to be the angle in the circle, so if its a full circle then 0...

Homework Statement I'm trying to help a friend with these two questions, but given that I haven't studied this material in over a decade, it's one of the topics I cannot recall at all. Convert the following from rectangular to polar coordinates: (a) x2 + y2 = x (b) y2 = 2x...

In the polar formula for arc length, ds^{2}=dr^{2}+r^{2}d{\theta}^{2}, what is the exact meaning of the r^2 term multiplying d{\theta}^2? Is it an initial distance from the origin? A final distance from the origin? The change in r from point a to point b? This baffles me to no end and nothing...

Homework Statement I have some questions want to be answered. 1. For rose, I believe there are two kinds, dealing with even peals and odd peals. My math professor confused himself in the lecture and could not tell us the right identification. The book is also helpless. For example, the form...

I can't seem to get the correct answer. I rechecked my calculations but no luck. Any help is appreciated. Thanks. Homework Statement Find the area inside the larger loop and outside the smaller loop of the limacon below. r = sqrt(3)/2 + cos(theta) Homework Equations A = (integral...

Homework Statement Find the area of the region enclosed by one loop of the curve. r = sin(10θ) I can't seem to get the correct answer...I checked every step. I was not sure what to integrate from but the polar graph of sin(10θ) should be similar to polar graph of sin(2θ). From pi/2 to 0...

I can't really understand something in spherical and cylinder coordinates let me start with polar coordinates first if we have for example x^2 + y^2 = 4 this is a circle with center (0,0) and radius 2 in polar coordinates x and y will be x = rcosφ y = rsinφ 0<=r<=2 0<=φ<=2π here φ is from 0...

Homework Statement Find the slope of the tangent line to the given polar curve at the point specified by the value of θ. r = 9sin(θ) θ = pi/6 Homework Equations dy/dx = (dy/dθ) / (dx/dθ) x=rcosθ y=rsinθ (sinx)^2 = (1/2)(1-cos2x) (cosx)^2 = (1/2)(1+cos2x) 2sinxcosx = sin(2x) The Attempt at...

Homework Statement Evaluate the integral integral from 0 to 1 of (integral from y to sqrt(2-y^2) of (3(x-y))dxdy) by converting to polar coordinates. Homework Equations x = rcos(theta) y = rsin(theta) The Attempt at a Solution By drawing a picture of the bounds, I...

Hey, I have the following integral: I = \int_0^\infty dx_1\ldots \int_0^\infty dx_{3N} \int_0^\infty dy_1\ldots \int_0^\infty dy_{3N}\Theta\left(1-\sum_{j=1}^{3N}\left(|x_j|^2+|y_j|^2\right)\right) Now I want to change to polar coordinates by the following substitution...

Find the volume under the cone z = sqrt ( x2+y2 ) and on the disk x2+y2 < 4. Use polar coordinates. Graphing x2+y2 < 4, I get a circle centered at 0,0 with radius of 2 So theta goes from 0 to 2pi Also, since x2+y2 < 4 This means that r^2 < 4 so -2 < r < 2...

Homework Statement \displaystyle\int\int\sqrt{4-x^2-y^2} dA R{(x,y)|x^2+y^2\leq4 .. 0\leq x} The Attempt at a Solution So far i have: \displaystyle\int^{\pi}_{0}\int^{r}_{0}\sqrt{4-r^2} rdrd\theta Solving i get...

Homework Statement This is a subtask. I was given a function, and then asked to convert it to polar coordinates. So I did, and I also determined the limit. However they ask me to do an epsilon-delta proof. The function is: f(x,y)=\frac{x^6 + y^8 + x^4y^5}{x^6 + y^8}, which converted to polar...

Hello, If we consider a Euclidean plane \mathbb{R}^2 with the ordinary inner product, and we "distort" it through a cartesian->polar transformation, how should I compute the shortest arc between two points (r,\theta) and (r',\theta') ?

Homework Statement Ok so I solved the problem, I think. I would just like to check my work. So the problem is: Use polar coordinates to find the volume of the given solid bounded by the paraboloids z = 3x^2 + 3y^2 and z = 4 - x^2 - y^2. Homework Equations r^2 = x^2 + y^2 x = r cos...

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.

Using polar coordinates to find the volume of a bounded solid[Solved] I found the equation of the boundary circle by setting z to 4 in the paraboloid. Then I did some work to get polar coords: x^2+y^2 = 1 x^2+y^2 = r^2 1-x^2-y^2 = 1-r^2 Then I set up my integral as such...

Homework Statement Ok so for circular motion we have v = w x r where w and r are vectors.. my question s very simple..what is the vector w? Homework Equations The Attempt at a Solution

Homework Statement Convert to polar coordinates to evaluate \int^{2}_{0}\int^{\sqrt(2x-x^2)}_{0}{\sqrt(x^2+y^2)}dydxThe Attempt at a Solution Really I'm just not sure how to convert the limits of integration. I know \sqrt(2x-x^2) is a half-circle with radius 1, but I'm not really sure where...

I'm studying for a maths test. I know that the second derivative of the position R(t) of a particle moving in the plane, in polar coordinates, is (r''-r(\vartheta')2)er + (r\vartheta''+2r'\vartheta')eo. o = \vartheta How to differentiate this to find R'''(t), in polar coordinates and...

Hi, so I scanned an image of the problem statement and my attempt at the solution. I don't know if I am headed in the right direction and need some guidance. This is my first post ever and I hope I am doing this properly. Thank you for any help you guys can provide.

Homework Statement Evaluate \int\intT (x^2+y^2) dA, where T is the triangle with the vertices (0,0)(1,0)(1,1) Homework Equations The Attempt at a Solution \int d\theta \int r^3 dr Thats how far I got, not really sure about boundries on r. First integrals boundrie should be 0 to pi/4. Is...

Hello, its been a pleasure finding you:smile: I have an asignment due to the end of this week and due to some problems, i hadn't found time to get to it so far. I have to calculate the exact solution of the Laplace equation in polar coordinates, in a hollow disk in the domain Ω where...

Hello, I posted a similar question long time ago, but after working on it I am still unable to arrive at a solution. Let's have a group of linear transformations (rotations in the xy-plane): R_\theta=\{ (\begin{array}{ccc} cos\theta & -sin\theta \\ sin\theta & cos\theta \end{array}) \\ ...

Homework Statement A particle of mass m is constrained to slide on the inside of a vertical smooth semi- circular ring of radius r. The position of the particle is described by a polar coordinate system whose origin is at the centre of the circle with axes along the orthogonal unit vectors...

Hey guys, I have attached the question with the diagram. So far i have found my magnitude of velocity = 90mm/s. im just really stuck now, i can't find my angle to find my components Vr and V(theta) I also know that you can solve this problem by finding a relationship between theta and "r"...

Hi I have a homework set due this week, 14 problems, I have done 11 of them, but these 3 are giving me trouble, help would be great :) Homework Statement 1.A cylindrical drill with radius 4 is used to bore a hole through the center of a sphere of radius 8. Find the volume of the ring shaped...

Homework Statement By transforming to polar coordinates, evaluate the following: \int^{a}_{-a}\int^{\sqrt{}{{a^2}-{x^2}}}_{-\sqrt{{a^2}-{x^2}}}dydx Homework Equations The Attempt at a Solution I can get the right answer to this but only after guessing that the inner limits...

Homework Statement Using Green's Theorem, (Integral over C) -y^2 dx + x^2 dy=____________ with C: x=cos t y=sin t (t from 0-->2pi) Homework Equations (Integral over C) Pdx + Qdy=(Double integral over D) ((partial of Q w.r.t. x)-(partial of P w.r.t. y))dxdyThe Attempt at a Solution I'm...

what'd I do wrong? I was told I didn't include the bound y<=x but that still hasn't helped me figure out where I miss stepped thanks -Ben

Homework Statement Particle is moving with velocity v= ui along the line y=2. What is its v in polar coordinates Homework Equations The Attempt at a Solution I think I'm being really stupid here but not entirely sure where to start. If you integrate to find position you have it as...

Homework Statement Find the area cut from the surface z = 2xy by the cylinder x^2 + y^2 = 6. [Hint: Set up the integral using rectangular coodinates, then switch to polar coordinates.] Homework Equations A = \iint \sqrt{{z_x}^2+{z_y}^2+1}dxdy = \iint...

Homework Statement Let the curve C be paramatized into polar coordinates given by: \[r\left( t \right)=\left( r\left( t \right)\cos \theta \left( t \right),\,\,\,\,\,r\left( t \right)\sin \theta \left( t \right) \right),\,\,\,\,\,a\le t\le b\] where r and theta is continuous derivatives...

Use polar coordinates to find the volume of the given solid inside the sphere x^2 +y^2 + z^2 = 16 and outside the cylinder x^2 +y^2 = 4 I know how to set up the the integral to find the volume inside the sphere but I am not quite sure how to also find the outside of the cylinder. Can someone...

Homework Statement Using polar coordinates, evaluate the integral which gives the area which lies in the first quadrant between the circles x^2 + y^2 = 4 and x^2 - 2x + y^2 = 0 Homework Equations The Attempt at a Solution for my integral i got 0<= theta <=pi/2 for the theta...

Homework Statement Give the equations for the plane polar unit vectors ^ ^ r and (theta) - - in terms of the Cartesian unit vectors ^ and ^ and hence show that i j - - ^...

I am going to have a test on polar coordinates next week. What are the most important things to remember?

Homework Statement Calculate the work W_{A B} done by the force F using Newton's laws (F=ma, etc), when a particle moves from the point A to the point B along the unit circle. The angle is \theta. No friction. How do you define kinetic energy in polar coordinates?Homework Equations...

Homework Statement ∫ e^(\pix^2) dx, with limits -∞ to ∞ Homework Equations ∫∫ dxdy = ∫∫ rdrdθ The Attempt at a Solution Hi, here's what I've done so far: Introduce a dummy variable y to get ∫∫ e^\pi(x^2 + y^2) dxdy, with limits -∞ to ∞ for both dx and dy...

Homework Statement We define the improper integral (over the entire plane R^2) I as a double integral [-inf,inf]x[-inf,inf] of e^-(x^2+y^2)dA as equal to the lim as a-> inf of the double integral under Da of e^-(x^2+y^2)dA where Da is the disk with the radius a and center at the origin...