Polar Definition and 1000 Threads

I've always been curious why points in polar coordinates are defined as (r,θ) when all equations (including parametric equations formed from them) are defined as r=f(θ). Considering that point in cartesian coordinates are defined as (x,y) where y=f(x). Also a,b=(r,θ) ∫1/2[f(θ)]2 further...

Homework Statement A tourist takes a tour through a city in stages. Each stage consists of 3 segments of length 100 feet, separated by right turns of 60°. Between the last segment of one stage and the first segment of the next stage, the tourist makes a left turn of 60°. At what distance...

Homework Statement Find the area in the polar curve r = sin2θ between 0 and \frac{\pi}{2}. The way to do this is to say the area of a tiny bit of this polar curve, dA = \frac{1}{2}r^{2}dθ so the integral is just \frac{1}{2}\int^{\frac{\pi}{2}}_{0}(sin2θ)^{2}dθ if we did say a function...

Homework Statement Hi, dispersion force exists in non-polar molecules due to instantaneous dipole. In polar molecule,the intermolecular force is the sum of dipole-dipole force and dispersion force. Polar molecules have permanent dipoles,this enables the oppositely charged end of molecules...

Homework Statement Change of coordinates from rectangular (x,y) to polar (r,θ). Not sure what's wrong with my working.. Homework Equations The Attempt at a Solution

Spherical, Cylindrical or Polar Coordinates Homework Statement I have attached an image of the problem. I know that the solution is number 1 but I'm having some difficulty understanding why. In solution one is it using cylindrical coordinates> My first response to this question had been to...

Question: Show that the system x'= x-y-x[x^2 + (3/2)y^2] y'= x+y -y[x^2 + (1/2)y^2] has at least one periodic orbit. I know that I need to apply Poincare-Bendixson Theorem. I can prove the first three points of it easily, but to create a trapping region, I believe that I need to...

Homework Statement \int_0^2 \int_0^\sqrt{2x-x^2} xy,dy,dx I know the answer, but how does the 2 in the outer integral become pi/2?? I'm fine with everything else, I just can't get this...

beautiful discovery! http://science.nasa.gov/science-news/science-at-nasa/2012/29nov_iceonmercury/

Homework Statement Take the double integration of http://webwork.usi.edu/webwork2_files/tmp/equations/08/1294e87299342c0ccfe2f8a97055da1.png when f(x)=sqrt(4x-x^2) Homework Equations x=rcos(theta) y=rsin(theta) The Attempt at a Solution I know I plug in the r*cos(theta) and...

Homework Statement Consider the complex function f (z) = (1 + i)^z with z ε ℂ. 1. Express f in polar coordinates. Homework Equations The main derived equations are in the following section, there is no 'special rule' that I (to my knowledge) need to apply here. The Attempt at a...

Homework Statement Given the equivalent impedance of a circuit can be calculated by the expression Z= (Z_1 Z_2)/(Z_1+ Z_2 ) If Z1 = 4 + j10 and Z2 = 12 – j3, calculate the impedance Z in both rectangular and polar forms. Homework Equations j2=-1 The Attempt at a Solution Z=...

Homework Statement Change the Cartesian integral to an equivalent polar integral and evaluate ∫∫dydx The bounds of the first integral (The outermost) are -5 to 5, and the bounds of the second (inner) are 0 to \sqrt{ 25-x^{2}}Homework Equations ∫∫dydx == ∫∫r(dr)(d\Theta) x^{2}+y^{2}=r^{2}...

I have a worksheet that due to missing the lecture I'm now stuck on. You are given a cartesian vector and told find the polar unit vecors and hence express the original vector as a linear combination of the polar unit vectors just found. I've searched resources online but feel that there is...

Any python/matplotlib experts out there?? This one has been driving me crazy all day. I have three vectors, azimuth, frequency and power, which I would like to histogram and plot on a polar axis. I can plot a scatter plot this way no problem but the histogram gets messed up somehow. An example...

Let's say we have a scalar function U in terms of r,theta and phi. why cannot this be the gradient at any point P(r,theta,phi)- partial of U wrt. r in the direction of r+partial of U wrt. theta in direction of (theta)+partial of U wrt. phi in the direction of (phi)?

I have this problem and I cannot even begin to start it. I have to hand it in today in a few hours, and I have been stuck on it for what seems like for ever. It reads: By using polar coordinates evaluate: ∫ ∫ (2+(x^2)+(y^2))dxdy R where R={x,y}:(x^2)+(y^2)≤4,x≥0,y≥0} Hint: The...

Hello all, I've been going through Bernard Schutz's A First Course In General Relativity, On Chapter 5 questions atm. Should the Christoffel Symbols for a coordinate system (say polar) be the same for vectors and one-forms in that coordinate system? I would have thought yes, but If you...

If we have to find the volume, written in polar cordinates, inside this sphere X2+y2+z2=16 and outside this cylinder x2+y2=4 How should I approach this? Could I take the sphere function and reqrite in polar cordinates z=√(16-X2-y2) which is the same as z=√(16-r2) But then I have...

Hi, I need help with this problem Evaluate the given integral by changing to polar cordinates ∫∫xydA where D is the disc with centre the origin and radius. My solution so far. I believe this would give a circle with radius 3 in xy plane. And then x=r*cos(θ) and y=r*sin(θ) So...

Homework Statement An impedance 8 + j7 Ω is connected in parallel with another impedance of 5 + j6 Ω. this circuit is then connected in series with another impedance, comprising a resistance of 5 Ω in series with a capacitive reactance of 7 Ω. The complete circuit is then connected to 150...

r = sin 2θ, r = cos 2θ. I'm having some trouble setting this up. $$1/2 \int_{\ -pi/8}^{\pi/8} cos^2 2θ~d\theta - 1/2 \int_{\ -pi/8}^{\pi/8} sin^2 2θ~d\theta $$ Which can be: $$\int_0^{\pi/8} cos^2 2θ~d\theta - \int_0^{\pi/8} sin^2 2θ~d\theta $$ Since there are 8 petals. $$8 \int_0^{\pi/8}...

r2 = 4cos(2θ) First I graph it. Then I set up the integral. _____π (1 / 2)∫ 4cos(2θ) dθ _____0 ________π = [sin(2θ)] ________0 I thought the limits ought to be π and 0, but that comes out to zero. I pick other limits and they come out to 0. My graph matches the one in the back of the book. I...

The question is in the paint document I wanted to know why they integrated from 0 to pi and not from 0 to 2pi

Dear all, As we know, there are two kind of capacitor polar and non polar. From that, I still did not know yet about specific application of them. Can give me something a clear of explanation of that? thank you reza_diharja

Hello I have the limit lim (x^9 * y) / (x^6 + y^2)^2 (x,y)---> (0,0) when I use polar the final result is limit = lim (r^6 cos^9 (theta) sin (theta) ) / (r^4 cos^6 (theta) + sin^2 (theta)) r--->0 and substituting r = 0 , it will give zero * I tried it on wolfram...

Homework Statement Step 1) I put the following into polar coordinates √(16-x2-y2)=√16-r2 Where r≤4 step 2 I solved for y in the original problem which is in the link y≤√(4-x2) step 3. I graphed the above function step 4. I put the above function in polar coordinates...

the question is showed below i know that x=rcos θ and y= rsinθ and x^2 + y^2 = R^2 but i just dun know how to find the locus is polar form any clue ?

Let S1*(S2*) be the polar cone of the set S1(S2) (http://en.wikipedia.org/wiki/Dual_cone_and_polar_cone). How can I show that if S1 is contained in S2 then S2* is contained in S1*. It looks obvious (especially if we think in R^2), but I do not find a way to prove it.

Homework Statement ∫∫e-(x^2+y^2) dA R Where R is the region enclosed by the circle x2+y2=1 First thing I did was graph the region where the function was enclosed. I saw that they didnt give a limitation to where the circle lied. So I automatically knew that d(theta) would lie on the...

Using tensors, I'm supposed to find the usual formula for the gradient in the covariant basis and in polar coordinates. The formula is \vec{grad}=[\frac{\partial}{\partial r}]\vec{e_{r}}+\frac{1}{r}[\frac{\partial}{\partial \vartheta}]\vec{e_{\vartheta}} where \vec{e_{r}} and...

Homework Statement Write z = 1 + √3i in polar form Homework Equations z = r (cos\varphi + sin\varphii) The Attempt at a Solution Found the modulus by |z| = √4 = 2 Now I am stuck on this part of finding the argument: Tan-1 (√3) now I am not sure how to go from that to...

Hi all, There is a question that asks? Determine the cube roots of 1 in polar form? Does that mean I can use De Moirve Formula? Stephen

Homework Statement Write the equation x^2 + y^2 = 1 + sin^2(xy) in polar form assuming x = rcos(\phi) y = rsin(\phi) 0<r, 0<= \phi < 2pi solve for r as a function of \phi The Attempt at a Solution (rcos(\phi))^2 + (rsin(\phi))^2 = 1 + sin^2(r^2cos(\phi)sin(\phi))...

Hi I have a function [e.g. f(r)] which I want to integrate over r and θ. What would be the integration form? Which one is correct? ∫∫f(r) drdθ OR ∫∫f(r) rdrdθ Please explain. Also, can it be said as area integration as well like the one in cartesian coordinate?

So we have the two ODE solutions are the cosine/sine and $r^n$ since it was a Cauchy Euler type. For the steady state, the solution is just a constant since it has to have period 2pi. But with $r^n$, how with lambda equal to zero does $\ln r$ come into play? If my question is hard to follow...

Homework Statement Using polar coordinates, show that lim (x,y)->(0,0) [sin(x^2+y^2)]/[x^2+y^2] = 1 Homework Equations r^2=x^2+y^2 The Attempt at a Solution I was able to get the limit into polar coordinates: lim r->0^+ [sin(r^2)]/r^2 but I'm not sure how to take this limit. I tried...

Hi everyone. I am a little desperated cause my exam is on monday and still much stuff to do. I don't get when I am supposed to use/consider radial and tranversal forces. Most excercises say "it rotates on the horizontal or vertical" I guess this is the info that tells me if there is...

I have never solved an equation in polar form. I am not sure with how to start. Solve Laplace's equation on a circular disk of radius a subject to the piecewise boundary condition $$ u(a,\theta) = \begin{cases} 1, & \frac{\pi}{2} - \epsilon < \theta < \frac{\pi}{2} + \epsilon\\ 0, &...

[b]1. For what value of α is the area enclosed by r=∅, ∅=0, and ∅=α equal to 1? [b]2. x=rcos(∅) y=rsin(∅) [b]3. x=∅cos(0) x=∅cos(α) y=∅sin(∅) y=∅cos(α) Don't know what to do after this

$$ p(r,\theta) = \frac{1}{2\pi}\sum_{n = -\infty}^{\infty}r^{|n|}e^{in\theta} = \frac{1}{2\pi}\left[\frac{1 - r^2}{1 - 2r\cos\theta + r^2}\right]. $$ So I produced the graph but it won't animate. MyR = Table[r, {r, 0, 1, .1}]; u[\[Theta]_] = 1/(2*Pi)*((1 - r^2)/(1 - 2*r*Cos[\[Theta]] + r^2))...

Homework Statement Hi, I'm trying to find the area of a circle in polar coordinates.I'm doing it this way because I have to put this into an excel sheet to have a matrix of areas of multiple circles. Here is an example of the problem. a= radius of small circle (gamma, r0) = polar coordinate...

Hi, I'm not sure how to integrate this equation where a, r0 and γ are constants.

Just starting up school again and having trouble remembering some mathematics. Here's the problem. Find the inner product of ⃗a = (1, 45◦) and ⃗b = (2, 90◦), where these vectors are in polar coordinates (r, θ). Thanks =) 1st post here btw.

Hi, I'm trying to find the area of a segment of a circle that is not at the origin. It will look similar to this picture below but I need to find the area enclosed by a circle. Using the polar equation of a circle provided by wikipedia: and integrating to find the area of a...

Hello all. I am trying to change: E = (1/r) ar To rectangular coordinate system. Where ar is a unit vector. So I know r = √(x^2 + y^2) i also think ar = ax+ay, where ax and ay are unit vectors along the x-axis and y-axis respectively. So that would give me: E = (1/√(x^2 + y^2)) (ax...

Not homework as such, just need some clarification. When finding \alpha do you have to take the signs into account when finding tan^{-1} x/a. Does it matter if a or x are negative? Next question is about quadrants 1: \theta = \alpha 2: \theta = \pi - \alpha 3: \theta = -\pi -...

If we divide the polar curve into infinitely thin sectors, the arc length of a single sector can be approximated by ds = \frac{dθ}{2π}2πr = rdθ. So why can't we model the arc length of the curve as \int^{β}_{α} rdθ It turns out that the correct formula is actually...

Homework Statement from the cartesian definition of angular momentum, derive the operator for the z component in polar coordinates L_z = -ih[x(d/dy) - y(d/dx)] to L_z = -ih(d/dθ) Homework Equations x = rcosθ y = rsinθ r^2 = x^2 + y^2 r = (x^2 + y^2)^1/2 The Attempt at...

Homework Statement r=5^theta theta goes from 0 to 2Pi Homework Equations Length= integral between a and b of sqrt(r^2+(dr/dtheta)^2)dtheta The Attempt at a Solution r^2=25^theta or 5^(2theta) dr/dtheta=5^theta (ln 5) (dr/dtheta)^2=25^theta+10^theta (ln 5)+...