Polar coordinates Definition and 569 Threads

Homework Statement Hey I have to create a six-pointed star and a hexagon with polar coordinates using MATLAB. I don't need help with using MATLAB, I just need help with the math. Note that I don't really need to know how the math sense this assignment is for a CSE course. I just don't...

Question: Given (-2*sqrt3) – ( 2*i) = 4*e^(i*7*pi/6) Perform the following: (a) Convention I: angle go from (0) to 2*pi. (b) Convention II: angle goes from (-)*pi to (+)*pi. = = = = = = = = = = = = = = = = = = = = = = = = = = = Part (a): Convention I: angle go from (0) to...

I don't remember ANYTHING from this section when I took Trig but we're finding the area of curves in the polar coords. Looking at the book they give us this equation r=2cos3\theta I can see, and I know how to figure out its a 3 leaf "rose" symmetrical about the theta= zero axis, but I can't...

Homework Statement I am doing even problems in my book to study and i want to check this answer to see if it is right. q: Find the area enclosed by one leaf of the three-leaved rose r=sin3(theta) Homework Equations A= integral 1/2 r2 d(theta) The Attempt at a Solution i used the...

Homework Statement Mass m whirls on a frictionless table, held to circular motion by a string which passes through a hole in the table. The string is slowly pulled through the hole so that the radius of the circle changes from l1 to l2. Show that the work done in pulling the string equals...

Homework Statement Transform to polar coordinates and evaluate... \int^{a/\sqrt{2}}_{0} dx\int^{\sqrt{a^2-x^2}}_{x}\sqrt{x^2 + y^2}dy Homework Equations x^2 + y^2 = r^2 x = r cos \theta y = r sin \theta I've been struggling to make sense of this problem, it should be easy, I'm...

Homework Statement integrate 1/((1+x^2+y^2)^2) dx dy Both x and y going from 0 to infinity Homework Equations x^2+y^2 =r The Attempt at a Solution After that I get 1/(1+r^2) ^2 Cannot visualize the function, do not know what the limits are. If I could have any help it...

Homework Statement Where the region is: D = {(x,y)| 0\leqx\leq2;0\leqy\leq\sqrt{}2x-x^2} Double integral over region D with f(x,y) = \sqrt{}x^2+y^2 and respect to dA Homework Equations Trig. Identities: x = rcos(theta) y = rsin(theta) x^2+y^2 = r^2The Attempt at a Solution First, I graphed...

Homework Statement Or any coordinates really. In the normal Cartesian plane, the center of mass is defined from the x, y , and z distance as follows \bar{x} = \frac{1}{Area(R)}\iint_R x dA \bar{y} = \frac{1}{Area(R)}\iint_R y dA \bar{z} = \frac{1}{Area(R)}\iint_R z dA Now is there one for...

I need to convert the Laplacian in two dimensions to polar coordinates. \nabla^2 u=\frac{\partial^2 u}{\partial x^2}+\frac{\partial^2 u}{\partial y^2} I am having problems with computing the second derivatives using the chain rule. For example, the first derivative with respect to x...

Homework Statement Sketch a graph of the polar curve whose points satisfy the following: As theta increases from 0 to pi/2, r decreases from 4 to 2. As theta increases from pi/2 to pi, r decreases from 2 to 0. As theta increases from pi to 3pi/2, r decreases from 0 to -1. As theta increases...

Homework Statement http://i1115.photobucket.com/albums/k554/shirozack/polarchange.jpg The Attempt at a Solution why is the limits for the polar angle pi/3 to pi/2? shouldn't it be pi/2 to pi/3? because x goes from 0 to 1/2, since x =rcos(T) 0 = cos(T) , T = pi/2 1/2 =...

i have no idea how to use the functions on here to ill try my best. \int(upper bound a lower bound 0)\int(upper bound 0 lower bound -sqrt(a2-y2) of the function x2y.dxdy firstly trying to map it out... i think its the quarter circle in the top left quadrant with boundaries 0 to a along...

I just want to see if my logic is sound here. If we have the paraboloid z=x2+y2 from z=0 to z=1, and I wanted a parametric form of that I think this should work for polar coordinates: \vec{r}(u,v)=(vcosu,vsinu,v^{2}) u:[0..2\pi],v:[0..1] Does this make sense?

Homework Statement Using polar coordinates, evaluate the integral which gives the area which lies in the first quadrant between the circles x2 + y2 = 256 and x2 - 16x + y2 = 0. Homework Equations The Attempt at a Solution Finding the intervals of integration for the polar coordinates. From the...

Homework Statement I don't understand why when we derive the velocity equation of motion in polar coordinates we start with position equal to R times R hat and not (theta times theta hat + R times R hat). Homework Equations none really.. The Attempt at a Solution Is there an assumption I'm...

Homework Statement A particle starts at (d, 0) in polar coordinates and has a velocity of \vec{v}=(u \sin{\theta} - v)\hat{r} + u \cos{\theta} \hat{\theta} where v > u Find the position vector of the particle as a function of time. Homework Equations \vec{v}=\frac{d\vec{r}}{dt}...

Hi. I have a pair of latitude and longitude (55.730397,12.358181) from Google Maps. I would like to convert it to POLAR COORDINATES in two-dimensional coordinate system. I am interested in the angle in the polar coordinates. I can't find any formula for this convertion? Thanks! /Taz

Homework Statement r = e^θ find arc length from (1,0) to origin Homework Equations ∫ab sqrt (r^2 + (dr/dθ)^2) dθ The Attempt at a Solution ∫10 sqrt ((e^θ)^2 + (e^θ)^2) dθ ∫10 sqrt (2(e^θ)^2) dθ ∫10 sqrt (2) (e^θ) dθ sqrt (2) ∫10 (e^θ) dθ need help converting limits in...

Homework Statement Hi, i am trying to find the div, grad and curl in cylindrical polar coordinates for the scalar field \ phi = U(R+a^2/R)cos(theta) + k*theta for cylindrical polar coordinates (R,theta,z) I have attempted all three and would really appreciate it if someone could tell me...

Homework Statement Semi circle of Radius R given. Find center of mass using polar coordinates, not double integrals. Homework Equations .5 intergral(r^2dpheta) (1/M) integral y dm r=R The Attempt at a Solution .5(2/piR^2) integral(R^3sinpheta do pheta) from 0 to pi, when I evaluate it I...

Homework Statement Consider a curve in R2 given in polar coordinates r=r(θ) for θ1<= θ <= θ2. Show that the line integral is equal to the integral from θ1 to θ2 of f(r*cosθ, r*sinθ) sqrt (r^2 + (dr/dθ)^2) dθ Homework Equations x= cos θ, y= sin θ The Attempt at a...

Homework Statement find limit if exist, or not then why f(x,y) = xy / sqrt(x2+y2) as (x,y) --> (0,0) The Attempt at a Solution can i change to polar coordinates x=rcost y=rsint so f(r,t) = rcostsint so as x,y tends to 0, r t will tend to 0 too?but cos(t) at 0 gives me 1...

Apparently one can deduce the form of divergence in polar (and spherical) coördinates using the theorem of Gauss and Ostrogradsky, namely that the volume integral over the divergence is equal to the flux integral over the surface. I can't see a way to do that, do you?

Homework Statement Hey am studing for my up coming exam and i am having trouble with transforming double intrgral to polar coordinates i have no idea where to start or anything so can someone explain it to me Homework Equations this is example \oint^{\infty}_{0}\oint^{\infty}_{0}...

Hi guys! I was reviewing some basic stuff in Special Relativity, specifically the part where it can be proven that a straight line connecting two events is the path that maximizes the interval between these two events. The proof is easy using the metric with cartesian coordinates ds^2 =...

Solving a PDE with Polar coordinates yu_x-xu_y=0 x=r\cos{\theta} \ \mbox{and} \ y=r\sin{\theta} u(r,\theta) Does u_x\Rightarrow u_r \ \mbox{or} \ u_{\theta} \ \mbox{and why?} Thanks.

Homework Statement \int_{y=-infinity}^{infinity} \int_{x=-infinity}^{infinity} (x^4+y^4)/(1+x^2+y^2)^4 dx dy Homework Equations i'm not sure what the new limits are after the transformation to polar coordinates and how to solve the integral. The Attempt at a Solution i have my...

Homework Statement Find the area of the infinitismal region expressed in polar coordinates as lying between r and r+dr and between theta and theta+dtheta Homework Equations A= [integral] (1/2)r^2 d[theta] The Attempt at a Solution To be honest I solved many of this kind of...

Homework Statement A plate with constant mass per unit area \rho is bounded by the curve (x^{2} +y^{2})^{2} = 9(x^{2} - y^{2}) . Find its moment of inertia about the x-axis. Homework Equations The Attempt at a Solution Okay well first I plugged in...

Homework Statement Bounded by the paraboloid z = 4 + 2x2 + 2y2 and the plane z = 10 in the first octant. Homework Equations The Attempt at a Solution Plugging in 10 for z I got 3=x2+y2. From this, I set 0\leqr\leq3\sqrt{}. I wasn't sure what to do with the first octant, but I...

Homework Statement Determine the Jacobian determinant for "polar" coordinates and use that to compute the intergral . . . Blah blah blah that's not the point. Homework Equations (x,y) maps by T to (r, theta) or (theta, r) detT = jacobian The Attempt at a Solution Anyways, first I...

I was overlooking a problem that my teacher solved and i can't understand a step see took i was wondering if someone you tell me how she got from this step Double integral rcos(o)(rsino)rto this Double integral (r/2)^3(2sinocoso)

r = cos(theta) in polar coordinates?? Hullo everyone! Hows it going? I am confused with how to interpret the graph of r = cos(theta) in polar coordinates. I tried graphing it manually. and this is how I interpreted it: r(0) = cos(0) = 1 r(pi/2) = 0 r(-pi) = -1 r(3pi/2) = 0 r(2pi)...

This question may be something of a dumb one. I feel I should know this, but well, I don't. I'm being asked to find the perimeter inside of the curve r=15sin(theta) and outside of r = 1 Setting up the equation I can do. If it were just an indefinite integral, this would be cake. My...

hi i need a affirm of curvature in polar coordinates. i need now please

Homework Statement Well the problem is a electromagnetism problem: I need to find the charge density. Given E= kr^3 r^ Homework Equations formula is gradient E=p/e0 The Attempt at a Solution They got the gradient of E to be 1/r^2 (d/dr) (r^2 Er) i have no idea how they did...

in this situation where apollo 13 is reentering the atmosphere, how would you determine what theta is in the polar coordinate system for velocity? [PLAIN]http://img37.imageshack.us/img37/7366/shuttlek.jpg Wouldn't the angle gamma be equal to theta since gamma is equal to the angle of the...

how to expand grad f * (p-p_0) in spherical polar coordinates in spherical polar coordinates: \nabla f = \frac{\partial f}{\partial r} e_r+ \frac{1}{r sin\theta}\frac{\partial f}{\partial \phi} e_{\phi}+ \frac{1}{r}\frac{\partial f}{\partial \theta} e_{\theta} p=(r,\phi,\theta) and...

Homework Statement Find the limit of lim_{(x,y) \rightarrow (0,0)} xy(\frac{x^{2}-y^{2}}{x^{2}+y^{2}}) Homework Equations The Attempt at a Solution We were supposed to switch to polar coordinates to solve this problem. Thus we get, lim_{(r) \rightarrow (0)} rcos\theta rsin\theta...

Homework Statement I've got this problem on polar coordinates which says: A particle moves along a plane trajectory on such a way that its polar coordinates are the next given functions of time: r=0.833t^3+5t \theta=0.3t^2 Determine the module of the speed and acceleration vectors for this...

I was perusing an astronomy homework site and came across a question in which they are asked to plot the positions of the 3 inner planets on polar graph paper. They are then asked questions about visibility and time of day in Earth's sky. The table: [FONT="Courier New"] Location Venus Earth...

Homework Statement I've got some trouble and doubts with polar coordinates. I have this exercise, with a rocket going upwards, with a given acceleration. So I need to find the polar equation for the given situation for the position, the velocity and the acceleration. How should I proceed? I...

Homework Statement When you substitute polar coordinates into a multivariable limit, do you treat theda as a constant when evaluating? (I know how to use polar coordinates to evaluate a limit but haven't learned what they are yet) Homework Equations The Attempt at a Solution

Homework Statement In Cartesian coordinates the magnitude of the velocity vector squared is |v|^2=V*V= Vx^2 +Vy^2 =(dx/dt)^2+(dy/dt)^2 Show that in polar coordinated |v|^2= Vr^2 +V@ ^2 Homework Equations The Attempt at a Solution Not really sure what the question is asking me to...

Homework Statement http://img138.imageshack.us/img138/4317/problem110.jpg Homework Equations The Attempt at a Solution Really I have no clue where to start on this guy. We did a problem sort of similar to this in class but we were given acceleration so we could use the form of...

Homework Statement Write the vectors B,D, and F in the figure in Cartesian form, with unit vectors. (See attachments) Homework Equations ax = a cos theta ay = a sin theta where a = magnitude of vector a, and theta = the angle vector a makes with the positive direction of the x axis...

Homework Statement Hi there. I must express the next region in polar coordinates: \{x\in{R^2:x^2+y^2\leq{2y}}\}So, this is what I did to visualize the region: Completing the square we get: x^2+y^2-2y\leq{0}\Rightarrow{x^2+(y-1)^2\leq{1}} Then, polar coordinates form: f(x)=\begin{Bmatrix}...

I appologise in the lack of distinction between curly d's and infinitesimals! All derivatives are partial and anything outside of brackets is an infinitesimal. also, I sincerely apologise for any dodgy terminology, but I am for the most part self taught (regarding calculus) :/ (also, 0 is my...

Homework Statement \int\int \frac{x^3}{x^2 + y^2}\,dxdy Use polar coordinates to evaluate the triangle R, with vertices (0,0), (1,0) and (1,1) Homework Equations \int\int f(r,\theta) r\,drd\theta r^2 = x^2 + y^2 x = rcos\theta y = rsin\theta The Attempt at a Solution I...