Polar Definition and 1000 Threads

Homework Statement 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. 2. The attempt at a solution My attempt as following: 2<=r<=4, and 0<=theta<=2pi So I do a double integral of...

Homework Statement Use the polar graph to determine the signs (+,-,0) of each derivative at the point labeled A. Homework Equations dy/dx= dy/dtheta= dx/dtheta= dr/dtheta= The Attempt at a Solution Hi people, I need help with this question. See the picture of the graph...

Is "radius" a misnomer in a polar equation? Often I see the description of "r" in a polar equation r = r(theta) as being "radius", but "radius" is a length, and here you can have a negative r. Hence "radius" is a misnomer, as far as I can tell. Perhaps it would be better described with some...

I am not understanding integration with polar coordinates, or at least visualizing what is happening. Here's the integral calculated in Wolfram: http://www.wolframalpha.com/input/?i=integrate+%28r%5E2%28cost%5E2-sint%5E2%29%29r+drdt+t%3D%280%29..%28pi%2F2%29+r%3D%281%29..%282%29+ the...

Homework Statement Use Polar coordinates to evaluate were C denotes the unit circle about a fixed point Z0 in the complex plane The Attempt at a Solution I've only used polar integrals to convert an integral in sin and cos into one in therms of z, find the residues and then use the...

Homework Statement r=2-3cosθ Find the tangent line at any point, and at the point (2,∏) Find the tangent line(s) at the pole Homework Equations Do I have to use x=rcosθ and y=rsinθ to convert it to rectangular to find slopes? The Attempt at a Solution Is the point 2∏ even a...

Homework Statement r=(1/(2+cos(θ))Homework Equations r=sqrt(x^2+y^2) rcosθ=x rsinθ=y The Attempt at a Solution Not sure what first step to take. This problem looks so simple, but I can't seem to get far on paper. Not sure if I should multiply both sides by 2+cos and then multiply both sides...

The cone centre is the z-axis and has base ρ=1 and height z=1, I'm looking at the lecture notes and it says the limit φ=0 to 2pi, z=0 to 1, ρ=0 to (1-z). Could someone tell me where the (1-z) comes from please? Why is it not 0 to 1?

Homework Statement The Cartesian coordinates of a point are given. (3,-5) (i) Find polar coordinates (r, θ) of the point, where r > 0 and 0 ≤ θ < 2π. (ii) Find polar coordinates (r, θ) of the point, where r < 0 and 0 ≤ θ < 2π. Homework Equations r^2=x^2+y^2 tanθ=(y/x) →...

Homework Statement let z=f(x,y) be a differentiable function. If we change to polar coordinates, we make the substitution x=rcos(θ), y=rsin(θ), x^2+y^2=r^2 and tan(θ) = y/x. a. Find expressions ∂z/∂r and ∂z/∂θ involving ∂z/∂x and ∂z/∂y. b. Show that (∂z/∂x)^2 + (∂z/∂y)^2 = (∂z/∂r)^2 +...

Homework Statement Im righting this down for my roommates since he's having tons of trouble trying to figure this out and I can't answer it. also sorry for having to hotlink it. http://i.imgur.com/afShz.jpg the equation is on the image since its very difficult to type it all out...

It is known that the area of a sector of a polar curve is \frac{1}{2}\int r^{2} d \theta This of course comes from the method of finding the area of an arc geometrically, by multiplying the area of the circle by the fraction we want \frac{\theta}{2\pi}\pi r^{2} Today I learned how...

1.The motors driving the fans of a large cooling tower must be represented in a dynamic simulation of a power plant auxiliary system. Each fan can be described as follows: Fan diameter = 4.5 meter No of blades/fan = 6 Fan RPM = 90 The fan blades have a tapering cross section. The fan...

Forgive me if this is in the wrong thread I'm new here. I am trying to plot an orbit in MatLab using Kepler's First law of motion. In polar form it works fine r(θ) = h^2/μ*(1/(1+e*cos(θ))) h = angular momentum μ = standard gravitational constant and e = eccentricity. The problem is I'd...

what is the area inside the graph of r=2sinθ and outside the graph of r=sinθ+cosθ? so i compute for the values of 'r',... but, i only got one intersection point which is (45°, 1.41). there must be two intersection points right? but I've only got one. what shall i do? i cannot compute for...

What type of bond is Sulfuric Acid (H2SO4(aq))? People tell me its ionic because the acid is made up of a polyatomic ion. However, many sources online say that the acid is polar. I can't seem to figure out which bond it is.

Staff was trying to understand a matter of calculation. I hope someone can explain me in detail how to solve this limit using polar coordinates: http://img36.imageshack.us/img36/2667/semttulokej.png

Homework Statement Let \hat r = <x_r , y_r> and \hat\theta = <x_\theta , y_\theta> Draw these vectors at points (x,y) = (1,0), (2,0), (3,0), (1,1), (0,1), (0,2). Here is the entire http://www.math.tamu.edu/~vargo/courses/251/HW5.pdf assignment so you can see what context it is in...

Homework Statement Homework Equations The Attempt at a Solution Do you see that 2 between A and the integral? There's no 2 in the above equation. I don't see where that 2 came from. Everything else is fine.

Hi all, I want to convert a curve from polar coordinates function to a parametric function. The function is: r = 2 \cdot \cos( 4\cdot\theta ) I want to convert this for ( x(t), Y(t) ). Why do I want this? Because I saw that wxMaxima make plots of parametric functions, but I don't know...

Hi all, As you may know, the interface of LaAlO3 and SrTi03 has received a lot of attention because of the presence of conducting electrons, superconductivity, and ferromagnetism. Because LaAl03 is a polar crystal, the polar catastrophe is often used as a first explanation for the presence of...

Let Q = theta Let z=reiQ z' = (a+ib)reiQ - z|z|2 |z|2 = r so z' = a*reiQ + ib*reiQ - r2eiQ Also z' = ireiQ The question asks for 2 differential equations, but I really have no idea where I'm going with this.. Any help? Thanks

Homework Statement What are the x- and y-components of the polar unit vectors \hat{r} and \hat{\theta} when a. \theta = 180° b. \theta = 45° c. \theta = 215° Homework Equations The Attempt at a Solution Please check if I'm correct, i'll just show my answer for a since the process is...

Homework Statement For a Foucalt Pendulum: Relative to horizontal Cartesian x and y axes fixed to the Earth (with x as East) the equations of motion for horizontal motion are: x′′ + ω02x -2ωy′ = 0 and y′′ + ω02y + 2ωx′ = 0 [where x′, x′′, y′, y′′ are first and second time...

Homework Statement Three charges are arranged as presented below. Q1= 5.00E-9C, Q2= 6.00E-9C and Q3= -7.00E-9C. http://img15.imageshack.us/img15/9250/physicskf.png D) Find the direction of the above electric field using the polar coordinate system 0°< θ <360° Homework Equations...

Homework Statement Find the area inside the inner loop of the limacon curve : r = 1 + 2cos(θ) Homework Equations A = ∫\stackrel{α}{β}(\frac{1}{2}r2)dθ The Attempt at a Solution i have the solution, my question is : how do you find α and β ? here α = 2π/3 and β = π A =...

Homework Statement Set up the integral for the area of the ellipse: \frac{x^2}{a^2} =\frac{y^2}{b^2} \le 1 in polar coordinates. Homework Equations maybe \int_\alpha^\beta \int_a^b f(rcos\theta , rsin \theta ) r \; dr \; d\theta or more likely \int_a^b \frac{1}{2} r^2 \; d\theta The...

Homework Statement Prove that the unit vector r{hat} of two-dimensional polar coordinates is equal to r{hat}= x{hat}cosθ + y{hat}sinθ and find the corresponding expression for θ{hat}. all I need is the last part... I'm just not sure what θ{hat} is? How do I go about doing this? Nothing in my...

Homework Statement Using f(z) = f(re^iθ) = R(r,θ)e^iΩ(r,θ), show that the Cauchy-Riemann conditions in polar coordinates become ∂R/∂r = (R/r)∂Ω/∂θ Homework Equations Cauchy-Riemann in polar coordinates Hint: Set up the derivative first with dz radial and then with dz tangential...

Hi guys, I'm trying to visualize what polar-coordinate-transform does to geometric figures in cartesian coordinates. It should be a function ℝ2→ℝ2, with domain R2-{0} and range r>0 and -\pi<θ≤\pi. I saw in Needham's Visual Complex Analysis a nice way to visualize such functions: he divides...

Homework Statement Given that z_{1}z_{2} ≠ 0, use the polar form to prove that Re(z_{1}\bar{z}_{2}) = norm (z_{1}) * norm (z_{2}) \Leftrightarrow θ_{1} - θ_{2} = 2n∏, where n is an integer, θ_{1} = arg(z_{1}), and θ_{2} = arg(z_{2}). Also, \bar{z}_{2} is the conjugate of z_{2}. Homework...

hi can anybody advise on this, need to find the angle out of the following 2300=2000+(0.5<x).(4<90) got as far as 300/4<90 = 0.5<x = 75<90= 0.5<x is this correct and anybody able to finish this off regards

If I have an integral: \int\int_{R} x^{2} + y^{2} dy dx Where the region R is the area enclosed by a circle centered on the origin of any given radius, is it possible to just convert x^2 + y^2 to r^2 and integrate from 0 to r over dr and 0 to 2 pi over d\theta? So it would become...

Ok, I thought the only two options in existence were Polar and Non-polar... and I'm being asked which ones are CHARGED? What does this mean? Example: NH4+ (ammonium), NO3- (nitrate), N2, O2, H2O Thanks!

Homework Statement Convert the polar equation: r = \frac{2}{ 2\,\sin \left( \theta \right) -3\,\cos \left( \theta \right)} to rectangular form Homework Equations x^2 + y^2 = r^2 x = r * cos(theta) y = r * sin(theta)The Attempt at a Solution I tried to to use the x = r cos(theta)...

Homework Statement How do you convert the rectangular coordinate points (1, -2) to polar form? note: rectangular is (x,y) polar is (r, theta)Homework Equations r^2 = x^2 + y^2 , x = rcos(theta) , y = rsin(theta) , tan(theta) = y/xThe Attempt at a Solution So basically, I tried getting it to...

Homework Statement Evaluate the double integral by converting to polar coordinates. ∫∫ arctan y/x dA; R is the sector in the first quadrant between the circles 1/4= x^2+y^2 and x^2+y^2=1 and the lines y=x/√3 and y=x. Homework Equations arctan y/x= θ The Attempt at a Solution...

Homework Statement Evaluate the surface integral. ∫∫S x^2*z^2 dS S is the part of the cone z^2 = x^2 + y^2 that lies between the planes z = 1 and z = 3. Homework Equations \int \int _{S}F dS = \int \int _D F(r(u,v))|r_u\times r_v|dA x=rcos(\theta) y=rsin(\theta) The Attempt...

Okay, so I have just broken into the polar coordinate system, and I like to derive things on my own to strengthen my intuition. I decided to try and derive the equation of an ellipse swiftly on my own, and had the high ambitions of eventually deriving the area of an ellipse with polar...

I was looking at the equation of a circle in polar coordinates on wikipedia, http://en.wikipedia.org/wiki/Polar_coordinate_system and I understand that a is the radius of the circle, and that (r0, phi) is the center of the circle. But I don't see what the r and theta refer to :(.

Homework Statement Given the two polar equations r=5-3cos(θ) and r=5-2sin(θ) find the area of the region common to both curves. Homework Equations A= 1/2∫ r^2 dθ The Attempt at a Solution i understand that i plug in the two equations into the equation, but i don't know how to find the...

i just need to know something about the integral with polar coordinates , to know the interval of the teta angle of any domain the proffesor said that we put the pen on the x-axis and move it , i for one moment was not focusing and the doctor had to go to another class can anyone explain ? thank you

I'm studying for my final and tutors/my professor isn't available over the weekend. Could someone please spend a little time to help me? My problem is stated as: Let R be the right half of the circle x2+(y-1)2=1. Use a double integral polar coordinates to find the area of the region R. I...

Homework Statement Let Q be the region bounded by r=sin(3θ) in the first quadrant. Find the area of Q. Find the average distance of points in Q from the origin. The Attempt at a Solution I thought I could calculate area like so: \int_0 ^{pi/3} \int_0 ^{sin(3θ)} sin(3θ) dr dθ This gives...

Transformation from Cartesian to spherical polar coordinates In dimensions: x=r sinθ cos \varphi and y= r sin θ sin \varphi z=r cos θ Show one example of: ∂z\alpha/ ∂xμ . ∂xμ/ ∂z\alpha = δ\alpha\beta Now here is my answer: δyx=(∂y/∂r . ∂r/∂x) + (∂y/∂θ . ∂θ/∂x) + (∂y/∂\varphi...

Homework Statement I'm trying to find the best solution for solving a problem in which I must form an operation with three vectors in polar form, ending with a sum in rectangular form. The operation is as follows: (5 \angle 0°) + (20 \angle -90°) - (6 \angle180°) = Homework Equations...

I wanted to know whether H2S is a polar compound and hence does it have a dp dp interaction. An answer sheet says the H2S only has id-id. If this is true can some one explain it to me? cause sulphur is definitively polar, and considering h2s's V shape, it should be a polar molecule, thus having...

Homework Statement Let F = <-y/(x2+y2, x/(x2+y2>. Recall that F was not conservative on R2 - (0,0). In this problem, we show that F is conservative on R2 minus the non-positive x-axis. Let D be all of R2 except points of the form (-x,0), where x≥0. a) If (x,y) is included on D, show that...

I'm having trouble figuring out how to find what "r" is. I know r is the radius, but how do I go about finding it? Like what do I look for in a particular problem?

Homework Statement "Consider the graph of r = e^{\theta} in polar coordinates. Then consider the graph of (\theta \cos{\theta}, \theta \sin{\theta}) where \theta \in \mathbb{R} on the Cartesian plane (x - y axis). How are the two graphs related? What relationship (if any) can we define between...