Polar Definition and 1000 Threads

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...

Homework Statement Microwave oven I. The glass window isn't important to the microwave oven's operation, but the metal grid associated with that window certainly is. The grid forms the sixth side of the metal box that traps the microwaves so they cook food effectively. What is the approximate...

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.)

Homework Statement Solve: \iint_{\frac{x^2}{a^2}+\frac{y^2}{b^2} \leq 1} \sqrt{1-\frac{x^2}{a^2}-\frac{y^2}{b^2}} dx dy Homework Equations Cartesian to Polar The Attempt at a Solution Well - this Integral should be solved as a polar function (the radical should be...

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?

-1-(under root)3 i here we find that r=2(hypotenuse) a=-1(base) b=-(under root)3 when i take sin theat= p/h=-(under root)3 / 2 theat from sin is -60 when i take cos theta = b/h =-1 / 2 which gives 120 now one is -60 and other is 120, which is the angel , i have to follow and what...

1.Where did I go wrong in finding the area enclosed inside r = 3 cos θ? Homework Equations I used the formula 1/2 ∫ ((f(θ)) squared dθ from alpha to beta The Attempt at a Solution I looked for the area of the semicircle from 0 to pi and then multiplied the whole thing by 2, since the...

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...

Canada obviously feeling inferior to Australia in the dangerous creature stakes have decided to go one better: "Canadian scientist aims to turn chickens into dinosaurs" http://www.physorg.com/news170426405.html

I have an integral \int \int_S x^2 + yz \ dS and wish to transform to spherical polar coordinates. How does dS become dS = r^2 \sin \theta d\theta d\phi ?? Where surface S is x^2 + y^2 + z^2 = 1

It's been a while since I studied calculus and basically I have a review sheet for a course I'm taking, but not a graded assignment. So, I was hoping if anyone knew a resource to point me in the right direction with a couple of problems: \int_0^\theta x^a dx Where a is not an element...

About the equation T=Ssqrt(T*T), what purpose does the sqrt(T*T) serve?

Homework Statement Compute the 4th roots of -16 in both Cartesian and polar form and plot their positions in the complex plane. Homework Equations z^1/n=(r^1/n)(e^i(theta)/n), (r^1/n)(e^i(theta)/n)(e^i2(pi)/n... The Attempt at a Solution How do I find the value of r, and theta??

Homework Statement Evaluate the square 0f 5e^(3(pi)i)/4 without using Cartesian form, and also the three different products. Homework Equations e^i(theta) = cos(theta) + isin(theta)? The Attempt at a Solution I have absolutely no idea here, nothing in my notes even begins to...

Homework Statement The equation of a conic in polar coordinates is: r = \frac{r_o}{1-\epsilon cos(\theta)}. \epsilon is the eccentricity, 0 for a circle, (0,1) for an ellipse, 1 for a parabola, and >1 for a hyperbola. What is this equation expressed in Cartesian coordinates...

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.

I want to caculate length of curve in Polar coordinate system like this: if r=r(a) then length of the curve is [SIZE="4"]∫r(a)da Is this right? if not ,why ? What's the right one ? I konw the way in rectangular coordinate system,I just want to do it in Polar coordinate system .

[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 reduce a current in its polar form 95 -46.37° by 20% Homework Equations The Attempt at a Solution When dividing a polar number by a scalar one you just divide the magnitude by the scalar, the phase will remain unchanged, so to reduce the polar value by 20%...

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...

Does there exist anything like a polar complex differentiation? So there exists a gradient equation in polar coordinates something like \nabla{f} = \frac{\partial f}{\partial r} e_r + \frac{1}{r}\;\frac{\partial f}{\partial \theta} e_{\theta} But this is not for a complex number f(z) where...

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...

Homework Statement Find the average area of an inscribed triangle in the unit circle. Assume that each vertex of the triangle is equally likely to be at any point of the unit circle and that the location of one vertex does not affect the likelihood the location of another in any way. (Note...

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?

So I know x=(r)cos(theta) and y=(r)sin(theta) As well as r^2 = x^2 + y^2 And (theta)=tan^-1 y/x or sin^-1 y/r or cos^-1 x/r If I want to convert the polar coordinates (7.6 , 285(degrees)) to rectangular coordinates, to the nearest hundredth, what would I do? And also...

for this problem, I've been given the vertices of the hyperbola as (4, pi/2) and (-1, 3pi/2). the question asks to find the polar equation of this hyperbola. so what i did was do a quick sketch of the graph. (4, pi/2) is essentially (0,4) and (-1, 3pi/2) is essentially (0,1). the midpoint of...

what is the difference between polar and non polar compounds

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...

Homework Statement Find area bounded by x^2 + y^2 = 1 and x^2 + y^2 = x + y Homework Equations The Attempt at a Solution from the second circle, we can see r^2 >= r cos t + r sin t so r >= cos t + sin t Limits are: cos t + sin t <= r <= 1 -pi/4 <= t <= 3pi/4 Doing the...

Homework Statement Consider the time-independent Schrodinger equation in spherical polar coordinates for a free particle, in the case where we have an azimuthal quantum number l=0. (a) Solve the radial equation to find the (unnormalized) radial wavefunction R(r). (b) Normalize R(r), using...

r= (15)/(3-2cos(theta)) I'm lost! Please Help! :confused:

Homework Statement Determine the expression for the area bounded by a polar curve and the criterion for integrability using both Darboux and Riemann sums. Homework Equations N/A The Attempt at a Solution Any suggestions on how to correct any errors in the following proof...

Volume of the intersection of two cylinders by cylinderical co-ordinates Homework Statement find Volume of the intersection of two cylinders by cylindrical co-ordinates The Attempt at a Solution IN the attached file I found it's 8(a^3)/3 It should be 16 not 8

Help me Evaluate the iterated intergal by converting to polar coordinate: http://www.ziddu.com/gallery/4894419/Untitled.jpg.html

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 Okay, this is probably a really simple thing but I'm just not able to wrap my head around it for whatever reason. I've got a second order system with feedback, where I've found the transfer function (and the real and imaginary parts of the transfer function), given by -AB =...

This is an extra credit problem for a take home test, so i will understand if no one feels comfortable helping me out, but any advice is greatly appreciated :biggrin: Homework Statement Compute the area enclosed by one loop of the graph given by r = sqrt(sin(3{theta})) Homework...

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...

Homework Statement we are given the intgral from 0 to 2( the integral from 0 to sqrt(1-(x-1)^2) of ((x+y)/(x^2+y^2))dydx, so convert to polar integral and solve Homework Equations The Attempt at a Solution i got integral from 0 to pi/2(integral 0 to 2cos(theta) of (x+y)/r dr...

Hi, I have two voltages given as v1(t) = 20cos(\omegat - 45) and v2(t) = 10sin(\omegat + 60) My task is to add them on the single form Vcos(\omegat + \theta) The first part is relativley easy: The phasors are v1 = 20\angle-45) and v2 = 10\angle-30) so i have 20\angle-45) +...

Homework Statement Use polar coords to evaluate the double integral x3 + xy2dydx from y = -(9-x2)1/2 to (9-x2)1/2, and x = 0 to 3 Homework Equations The Attempt at a Solution So the region is a half circle of radius 3, centered @ the origin, with only the possitive x side...

Homework Statement Find the area inside one leaf of the four-leaved rose r = cos2xHomework Equations A = 1/2 antiderivative abr2 dxThe Attempt at a Solution I just need help in finding the lower and upper limits of integration. But besides that, I know how to do the rest. If my integration is...

Homework Statement I need to convert this to a polar coordinate \vec{F} = 5xz\vec{i} + 5yz\vec{j} + 4z^3\vec{k} Homework Equations The Attempt at a Solution I have no idea to do this, can someone help?

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 convert line one to polar integral and then evaluate see problems 16 attachement Homework Equations r^2=y^2+x^2 The Attempt at a Solution I changed to polar and evaluated the double integral but I come up with an answer of negative pi which seems odd since it...

Homework Statement convert double integral from line one to polar integral and then evaluate see problem 12 attachment Homework Equations y=rsinx x=rcosx r^2=x^2+y^2 The Attempt at a Solution see problem 12 attachment I calculate a area of zero. are my limits wrong and if...

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...

Had a trig exam today, got all problems right except for one that seemed to stump me: Change from polar form to rectangular coordinate form: r = 1 - 2cosθ I got the graph right I know that, but I couldn't figure a way to change it over. It kind of bugs me because I went through my entire...