Polar coordinates Definition and 569 Threads

Homework Statement http://img162.imageshack.us/img162/9831/97118623.jpg Homework Equations The Attempt at a Solution I first drew R, and from the circle equation, I know the radius of the circle is 12.5. Since the region is in the first quadrant, that'll mean that my limits of...

Homework Statement Rewrite by converting to polar coordinates, carefully drawing R. \int^{2}_{0}\int^{\sqrt{2x-x^2}}_{0}\sqrt{x^2+y^2}dydxHomework Equations The Attempt at a Solution I believe I have the inside part of it right. What I did was replace the x^2 and y^2 in \sqrt{x^2+y^2} with...

Homework Statement using only trigonometric identities, derive the differential area element in polar coordinates? any help with this problem or at least a start? Homework Equations i found this so far dA=(dr)(rd θ) The Attempt at a Solution i have tried to figure this one out...

I came across this example on the net : We are integrating over the region that is the area inside of r = 3 + 2 sin θ and outside of r = 2, working in polar coordinates (r,θ). What is the limits of integration for θ? # I already know the answer. But I have no idea how to arrive at the...

Hi there, I am getting confused about how to work this out. I know that to convert cartesian coordinates to spherical coordinates you can use: theta=arccos(z) phi=arcsin(y/sin(theta)) my problem is that I have a list of coordinates, let's call them THETA and PHI. I change them into X,Y,Z...

Any web resources regarding changing the variable of integration from cartesian to polar coordinates that goes beyond the basic : x = r cos theta y = r sin theta r = sq rt (x^2 + y^2)I totally don't get how to find the limits of integration using polar coordinates and my undergrad textbooks...

Homework Statement calculate: \oint \frac{2-y}{x^2+(y-2)^2} dx + \frac{x}{x^2+(y-2)^2} dy where y = \sin{t} + 2, x = \cos{t}, 0 \leq t \leq \pi Homework Equations Green's Theorem. The Attempt at a Solution In what order should I do everything? I need to find the derivaties...

What is e^(-r/a) in spherical polar coordinates, and what are the bounds for the integrals? (I need to know to norm a wave fxn given as e^(-r/a) in 3 dimensions.)

Suppose we investigating the limit of a function on R^2 as (x,y) tend to (0,0). We convert the function into polar coordinates. Then "(x,y) tend to (0,0)" is equivalent to "r tend to 0"? Theta (the angle) does not matter?

Homework Statement I have to evaluate the surface integral of the following function over the top hemisphere of a sphere.Homework Equations \sigma (x,y,z) = \frac{\sigma_0 (x^2+y^2)}{r^2} z = \sqrt{r^2-x^2-y^2} \iint G[x,y, f(x,y)] \sqrt{1+ \frac{\partial f}{\partial x}+ \frac{\partial...

I calculated the christoffel symbols and know that I have them right. I want to take the covariant derivative of the basis vector field e_{r} on the curve s(t) = (a, t/a). I differentiate it and get s' = (0, 1/a) and according to the metric, this is a unit vector because a will always be equal...

Homework Statement \int\int(rsin2\vartheta)drd\vartheta sorry i don't see how to put the bounds in but they are 0<\vartheta<\pi/2 and 0<r<2acos\vartheta Homework Equations I know that r=sin\varthetaThe Attempt at a Solution Im really not sure where to start my text is terrible. I really...

Dear All, How do you derive both equations below. Let r be the position vector (rcos(θ), rsin(θ)), with r and θ depending on time t. These equations can be found in wiki under polar coordinates.

[b]1. Was wondering if anyone could help me confirm the polar limits of integration for the below double integral problem. The question itself is straight forward in cartesian coordinates, but in polar form, I'm a bit suspect of my theta limits after having sketched the it out. any help much...

Homework Statement Find \int{\int_{D}x dA} where D is the region in Q1 between the circles x2+y2=4 and x2+y2=2x using only polar coordinates. The Attempt at a Solution Well, the two circles give me r=2 and r=2 cos \theta, and the integrand is going to be r2cos \theta, but I have no...

Homework Statement Find the gradient vector of: g(r, \theta) = e^{-r} sin \theta Homework Equations The Attempt at a Solution I know how to get gradients for Cartesian - partially derive the equation of the surface wrt each variable. But I have no idea how to do it for...

This is more of a general question, really no math involved. Since polar coordinates are, (theta, r), the direction of the vector is theta, and the magnitude is r, in polar coordinates, does a vector represent rotational force?

Homework Statement Hey i know that we can change it by using r^2=X^2+y^2 and tan(theta)=y/x; but finding some problems in converting the area surrounded by X=0; Y=0; x+y=1; x+y=2 to polar coordinates . yr of course you can convert X=0 to theta=pi/2 and Y=0 to theta=0; But i...

Hi, I have the fields for a rectangular waveguide in terms of cartesian components, that is, Ex, Ey, Hx, Hy. I need to convert these to polar components in terms of r and theta. I've done this the other way around, converted a circular waveguide field which was written in terms of r and theta...

Homework Statement graph the polar function r=2cos\theta (-\pi/2 \leq \theta \leq \pi/2) sorry that last theta/2 should be pi/2. new to this math text Homework Equations The Attempt at a Solution I graphed the positive part right, I think. it seems to trace a half circle. I...

Been looking over past exam questions and came across this one. Its in polar coordinates: A particle P describes the curve r=be^[Zcot(a)]. Show that the velocity and acceleration vectors have angles a and 2a with OP (O is the origin). Z is actually theta, the angle the position vector...

Homework Statement Evaluate by changing to polar coordinates Homework Equations Can't figure out how to make the integral stop after the sqrt(9-x^2) \int_0^\frac{3}{\sqrt(2)} \int_x^{\sqrt(9-x^2)} e^-(x^2+y^2) dy dx The Attempt at a Solution I'm not sure where to really start on this one...

Homework Statement The solid bounded by the parabolids z = 3x^2 + 3y^2 -7 and z = -x^2 -y^2 + 9 Homework Equations The Attempt at a Solution Ok so i set the two z equations into polar form and came up with 3r^2 = 7 and r^2 = 9 I thought that r went from (7/3) ^(1/2) to 3 and...

Homework Statement Consider the vector potential A = cr * [(sin theta)^2 * (cos fi) * (sin fi) + (cos theta)^2 ) er + (sin theta) cos (theta) * [(sin fi) (cos fi)  − 1] e theta + {(sin theta) (cosfi)^2 } efi er: in the er direction e theta: in the e theta direction...

http://containsno.info/mq.JPG The problem says evaluate the double integral (x + y)dA over the dark region shown in the Figure: I set up the integrals like this: \int_{0}^{\pi /2}\int_{2sin\o }^{2} (rcos\o + rsin\o)rdrd\o Is this correct? Thanks a lot everyone

1. Homework Statement [/b] Let e_r=(cos\theta,sin\theta) and e_theta=(-sin\theta,cos\theta). Let P(r,\theta) be a point with e_r and e_theta at that point. What can you say about the three quantities (e_r, e_theta and the point P) as r and \theta vary? Homework Equations r: distance...

Homework Statement Find the area inside the lemniscate r = 2sqrt(sin(2theta)) Homework Equations Integral from a to b of (1/2)[f(theta)]^2 d(theta) The Attempt at a Solution I tried integrating from 0 to 2pi and got an area of 0. Then I tried integrating from 0 to pi and still...

1. The question was find the area between the curves using DOUBLE Integrals Area between: r = sin theta r = cos theta well to draw them i made them into cartesian form by r^2 = rsin theta r^2 = rcos theta so x^2 + y^2 = y x^2 + y^2 = x completing square 1) x^2 + (y -...

Hey Everybody. for the system: r' = r(1-r) \theta' = 1 with r(0) = x; \theta(0) = 0 ; the answer is r(t) = \frac{xe^{t}}{1-x+xe^{t}} \theta(t) = t This answer was given in class as part of a process, and I can't remember how that answer is calculated. Can someone help me?

Homework Statement The rectangular and polar coordinates of a point are (x,y) and (r, Theta ) and theta equals 67 degrees Homework Equations ?? The Attempt at a Solution I know nothing about this does anyone know an equation or anything PLEASEE thanks.

Homework Statement v is in polar coordinates and i want to fin u(x,y) knowing that v(r,theta)=u(rcos(theta),rsin(theta)) therefore, u(x,y)=v(sqrt(x^2+y^2), arctan(y/x)) v(r,theta) = 9+18cos(2(theta))-9sin(4(theta)) question: what is u(x,y)? Homework Equations The Attempt at a...

Homework Statement \int^{0}_{-3}\int^{\sqrt{9 - x^2}}_{- \sqrt{9 - x^2}} \sqrt{1 + x^2 + y^2} dy dx Homework Equations x = rcos(theta) y = rsin(theta) The Attempt at a Solution By making \sqrt{9 - x^2} = y then changing it to polar coordinates, I got r to be +/-3 but I'm...

Homework Statement Consider the volume of a solid bounded by the cone: z = sqrt(x^2 + y^2) and the top half of the sphere x^2 + y^2 + z^2 = 18 that is for z >= 0 Using cylindrical coordinates, express the volume as a double integral. Homework Equations easy to sketch.. we can...

Homework Statement ok change the region R = { (x,y) | 1 <= X^2 + y^2 <= 4 , 0 <= y <= x } to polar region and perform the double integral over region R of z=arctan(y/x)dA Homework Equations r^2 = x^2 + y^2, x = r*sin(@), y = r * cos (@) The Attempt at a Solution i got R = {...

Homework Statement The vector \vec{E}_n is the vector sum of the two vectors \vec{E}_r and \vec{E}_{\theta}, which are perpendicular to each other (see attached picture). Calculate the magnitude of \vec{E}_n. The Attempt at a Solution E_n=E_r\cos(\theta)+E_{\theta}\sin(\theta) But...

Hello, this question is about symmetry of polar coordinates. For a polar-curve to be symmetric around the x-axis we require that if (r,a) lies on the graph then (r,-a) or (-r,Pi-a) lies on the graph. To be symmetric about the y-axis we require that (-r,-a) or (r,Pi-a) lies on the graph...

Homework Statement Given r = 2tan(theta)sec(theta) Find cos(theta) then use inverse key to find sec(theta) The answer given in the solution guide is y = 1/2 x^2 Attempt at solution Since tan = sin/cos and sec = 1/cos We have r = 2sin/cos * 1/cos So rcos^2 = 2sin rcos^2 is defined...

Homework Statement I have a problem I hope you guys can help me with. It's quite simple I think, but there is one thing that I can't figure out. Homework Equations I have to use polar coordinates to evaluate this integral: See image The Attempt at a Solution I really don't have...

Homework Statement Use polar coordinates to find the volume bounded by the paraboloids z=3x2+3y2 and z=4-x2-y2Homework Equations The Attempt at a Solution Somehow, through random guessing, I managed to get the right answer, it's just that I don't understand how I got it. Also, because the z is...

I have a function f(r, \phi, \vartheta) = 3cos\vartheta. Evaluating the repeated integral of this function over the surface of a sphere, centered at the origin, with radius 5, I have come up with 0 as my result. I'm not sure if this is correct. I've double checked my calculations, and tried...

Homework Statement Find The length of r=sin³(x/3) 0<x<3pi/2 2. The attempt at a solution well first i found r'=3.cos(x/3).1/3.sin²(x/3)=cos(x/3)sin²(x/3) r²=cos²(x/3)sin^4(x/3) then i put the formula integral of radical (r'²+r²)dx and I'm stuck here any help?

Homework Statement we have this diagram were it says that the change in the unit vector der equals in magnitude the change in the angle betwen the two unit vectors er. Could someone explain me why is this? I include the diagram named Polar coordinates.

Express the following vector field in spherical coordinates. (The answer should be in a form that uses the unit vectors of the curvilinear coordi- nate system and coefficient functions that are written in terms of the curvilinear coordinates.) \underline{F} = -y \underline{i} + x...

Homework Statement A mass follows the path of a cardioid r=1+sinφ with given speed, what is its period? Homework Equations The Attempt at a Solution I attempt to do an integral on polar coordinates to find the distance covered by the mass first. The integral I derived is \int_0^{2\pi}...

Ok, here is my problem. I haven't taken anything vector related since at least one year ago. And back then, I wasn't such a good student.. So now my past has come back to haunt me.. I still have some basic notions, but other than that, I pretty much forgot things...

Homework Statement Compute \nabla \cdot \nabla f in polar coordinates.Homework Equations The Attempt at a Solution It seems like a straightforward dot product yields \nabla \cdot \nabla f = {\partial^2 f \over \partial \rho^2} + {1 \over \rho^2} {\partial^2 f \over \partial \theta^2} +...

Homework Statement \frac{\partial^2f}{\partial x^2}+\frac{\partial ^2f}{\partial y^2}= 0 Homework Equations Show that the equation above is equal to: \frac{\partial^2f}{\partial r^2}+\frac{1}{r^2} \frac{\partial ^2f}{\partial \theta^2} + \frac{1}{ r} \frac{\partial f}{\partial r}= 0...

Why is \nabla\cdot\vec{A}=\frac{1}{r}\frac{\partial}{\partial r}(rA_{r})+\frac{1}{r}\frac{\partial}{\partial \theta}(A_{\theta}) Where \vec{A}=A_{r}\hat{r}+A_{\theta}\hat{\theta} And \nabla=\hat{r}\frac{\partial}{\partial r}+\hat{\theta}\frac{1}{r}\frac{\partial}{\partial \theta} Instead of...

Homework Statement I need to evaluate this limit by converting to polar coordinates: lim (x,y) -> (0,0) of (x^2 + xy + y^2) / x^2 + y^2 Homework Equationsx = rcos(theta), y = rsin(theta) The Attempt at a SolutionSo switching to polar I get: [(rcos(theta))^2 +...

Homework Statement http://img127.imageshack.us/img127/2695/coord2pq5gm6.jpg Homework Equations \underline v = \dot r\;\underline e _r + r\dot \theta \;\underline e _\theta \underline a = \left( {\ddot r - r\dot \theta ^2 } \right)\underline e _r + \left( {r\ddot \theta + 2\dot r\dot...