Polar Definition and 1000 Threads

Homework Statement Show that the solution x(t) = Ge^(iwt), where G is in general complex, can be written in the form x(t) = Dcos(wt - \delta). D(w) and \delta(w) are real functions of w. Homework Equations z = Ae^(i\phi) The Attempt at a Solution So I know I should start by...

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...

I just did a quiz in a lecture and walked out crying. There was one question (which probably seems very easy to most :/ ) were you had to convert polar equations to cartesian ones. We also had to draw the cartesian graphs (2D). a) rcos(th) b)r=2asin(th) c)r^2sin2(th)=2k...

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: Location Venus Earth Mars 1 280...

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 Homework Equations The Attempt at a Solution Please tell me if I am wrong. I suspect about the ranges. Are my range corrrect?

This particular problem is just confusing me in the setup. I need to find the area that is inside both: r=sqrt(3)cos(theta) and r=sin(theta) It makes a petal type shape. I was beating my head around for a while, but I reasoned that since the equation used to find the area cuts out in a straight...

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 H(F) = 5/(1+j2piF/10) Rewrite in polar form, that is, in terms of magnitude and phase. Homework Equations The Attempt at a Solution phase is the 2piF/10 but I'm not sure how I account for it being on the bottom of the fraction

Well this problem started off simply enough. I was given this function: r=2cos(3\theta) And I had to find the area bound by it. I sketched it out from zero to 2pi and got this...

I know that a complex number can be written in form of a+bi and r(cos(theta) + isin(theta)) but I don't understand the the representation of it as r*e^(i * theta) also

Homework Statement Well, I've made a double limit using the polar forms. The thing is the limit is wrong, I've made a plot, and then I saw that the limit doesn't exist, and what I want to know is what I'm reasoning wrong, and some tips to get a deeper comprehension on this limits, and on what I...

I'm having issues getting converting Polar functions to Cartesian functions. Take for example: rcos(\theta)=1 I just figured that since it was going to always equal the same thing, and because x=rcos(\theta) that the Cartesian equation was x=1, and I was right. However logic fails...

It seems to me that integrating a polar equation should give you the arc length of the curve, rather than the area under it. This is my reasoning: A polar equation is in the form of: (1) r = f(\theta) The arc length of a segment of a circle where the radius is constant is given...

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 polar equation for the graph y = x. Homework Equations x = r cos \theta y = r sin \theta The Attempt at a Solution I came up with \theta = \pi/4 because at \pi/4, the x and y coordinates match each other. I'm not sure this is correct, though.

Homework Statement r = 3 sin \vartheta 0 \leq \vartheta \leq \pi/3 Homework Equations Arc Length: \int \sqrt{r^{2} + (dr/d\vartheta)^{2}}d\vartheta The Attempt at a Solution r^{2} = 9 (sin \vartheta)^{2} = 9 (1/2 - cos 2\vartheta/2) r^{2} = 9/2 - 9/2 cos 2\vartheta...

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...

Express the following in cartesian curves in polar form i) 4x-5y=2 Not sure how to do this ii) (x-3)^2+(y-4)^2=25 r=9cos16(theta) Is this correct ? Any help would be great

Homework Statement HI Can anyone help me in finding out the polar moment of inertia of a hollow shaft with 3 circular slots . Its used in design of DIVERTERS in oil and gas application. Homework Equations The Attempt at a Solution

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}...

Find the area of the region in the plane enclosed by the cardioid r = 4+4\sin{\theta} The book explains that "Because r sweeps out the region as {\theta} goes from 0 to 2{\pi}, these are our limits of integration."

I am always a little confuse in polar, cylindrical and spherical coordinates in vector calculus vs cylinderical and spherical coordinates in vector fields used in Electromagnetics. I want to clarify what my finding and feel free to correct me and add to it. A) Vector calculus: We use x =...

Homework Statement A particle follows a trajectory given as R = Aθ, where θ is the polar angle.in a horizontal plane. The trajectory is such that the walls are vertical and the particle moves in a groove made by them. The particle remains in contact with both the walls throughout its motion...

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...

Homework Statement the circle travels clockwise from (0,-1) to (0,1) write down the parameterization in term of tHomework Equations The Attempt at a Solution x=cost(t) y=-sin(t) i'm not sure about the sign of the polar coordinate, how to find the sign?

Hi, So, I was doing my physics summer work and had no idea what the following question was talking about: Homework Statement For the following polar coordinate points: (4, 0) (4, 60) (4, 90) (4, 135) (4, 180) (4, 270) Describe the locus of points for which a) r = 4 b) r = a...

Homework Statement With a > 0, b > 0, and D the area defined by D: \frac{x^2}{a^2} + \frac{y^2}{b^2} \leq 1 Change the integral expression below: \iint\limits_D (x^2+y^2) dx\,dy by using x = a r cos θ, y = b r sin θ. After that evaluate the integral. The Attempt at a Solution...

Homework Statement The planets travel in an elliptical orbit with the sun as a focus. Assume that the focus is at the pole, the major axis lies on the polar axis and the length of the major axis is 2a. Show that the polar equation of orbit is given by r=\frac{(1-e^2)a}{1-e\cos\theta} here's...

I am having trouble understanding how (2x - x2)1/2 becomes 2 cos θ. Thanks

Good morning, I have a doubt about the differentiation of the polar equation of an orbit: r=\frac{p}{1+e\cos\nu} It represents the relative position of a planet with respect to the central body. Here, p is the parameter, e is the eccentricity and r is the radius of the planet measured from...

Homework Statement Convert the polar equation r = 2(h cos θ + k sin θ) to rectangular form and verify that it is the equation of a circle. Find the radius and the rectangular coordinates of the center of the circle. Homework Equations The Attempt at a Solution First, I...

Homework Statement Convert the polar equation to rectangular form. r=2sin(3θ) Homework Equations The Attempt at a Solution I can expand this out to r=2(\sin\theta\cos2\theta+\cos\theta\sin2\theta) multiply both sides by r...

Homework Statement Find the area of the region inside: r = 9 sinθ but outside: r = 1 Homework Equations The Attempt at a Solution r = 9 sinθ is a circle with center at (0, 4/2) and radius 4/2 while r= 1 is a circle with center at (0, 0) and radius 1. The two curves intersect...

Homework Statement Show that the function f(x,y)= xy/sqrt(x^2+y^2) is continuous at the origin using polar coordinates. f(x,y)=0 if (x,y)=(0,0) Homework Equations r=sqrt(x^2+y^2) x=rcos(theta) y=rsin(theta) The Attempt at a Solution So, converting this equation to polar...

Homework Statement Compute the indicated solid in POLAR COORDINATE using double integrals. Below z = 4 - x^2 - y^2, z = x^2 + y^2, between y = x and y = 0. Homework Equations The Attempt at a Solution First of all, the integrand is z = 4 - x^2-y^2 which in polar is 4 - r^2 The...

Homework Statement Compute the volume of the indicated solid Below z = sqrt(x^2+y^2), above z = 0, and inside x^2 + (y-1)^2 = 1Homework Equations The Attempt at a Solution My professor solved this in class but I didn't understand why deta is from -pi/2 to pi/2. It is obvious that the...

Homework Statement Hi, I would like to know what is the right way to write continuous deltas standing in a circle of radius a? Homework Equations The Attempt at a Solution I am not sure weather it's δ(r-a) or is it δ(r-a)/|r-a| Thank you

Homework Statement I was looking at the book's example. The author left the final integration as an exercise, and I was attempting it. 1/2 integral of [ (2 - 2sin(delta) )^2 - 0 ] d delta from 0 to 2pi for the sake of work, i will let x = delta (2-2sin(x))^2 => 4 - 8sinx + 4sin^2(x) and i...

Homework Statement "Find the area of the region which is inside the polar curve r=5cos(theta) and outside the curve r=4-3cos(theta)." Homework Equations The Attempt at a Solution I keep coming up with 18.708, but it says that's incorrect. I don't know what I'm doing wrong...

Homework Statement Use polar coordinates to find the volume of the given solid. Inside the sphere x²+y²+z²=16 and outside the cylinder x²+y²=4. Homework Equations x=rcosΘ,y=rsinΘ, x²+y²=r² The Attempt at a Solution 2∫∫ (√(16-r²)r)drdΘ R{(r,Θ)l 0<Θ<2∏, 2<r<4} I was...

Homework Statement evaluate the iterated integral by converting to polar coordinates integral, integral x2dxdy, the limits are 4 to 0 for the outer integral, and /sqrt(4y-y2) to 0 for the inner integral. Homework Equations The Attempt at a Solution well...

Homework Statement Find the area of the region between the inner and outer loop of the limicon r=2cos(x)-1 Homework Equations A=(2(1/2)small circle)-(2(1/2)large circle) The Attempt at a Solution I don't even know where to start with this question because I can't figure out the...

Homework Statement Find the length of the cardioid with equation r = 1 + cos (theta) located in the first quadrant Homework Equations f (theta) = 1 + cos (theta) f'(theta) = -sin (theta) s = antiderivative (0 to (pi/2)) sq rt (f(theta)^(2) + f'(theta)^(2)) d(theta) The Attempt at...

Homework Statement See attachment. Change the Cartesian integral into an equivalent polar integral, then evaluate the integral. I have no problems at all converting the actual function I am integrating or the integration itself, it is just the limits I cannot do. I've posted two...