Polar Definition and 1000 Threads

I'm trying to express the polar rose as an implicit function: r(t)=sin t x = sin t * cos t y = sin^2 t Since sin t * cos t = (1/2) * sin 2t and sin^2 t = (1/2) * (1-cos 2t) (2x)^2 + (1-2y)^2 = 1 4x^2 -4y + 4y^2 = 0 When I plot this, Maple plots a circle, where have I gone wrong?

Homework Statement Give the equations for the plane polar unit vectors ^ ^ r and (theta) - - in terms of the Cartesian unit vectors ^ and ^ and hence show that i j - - ^...

I am going to have a test on polar coordinates next week. What are the most important things to remember?

Expressing Impedance in Polar and Complex Number form HELP! Homework Statement A Single Pahse, 50Hz, A.C. Generator is to be used to supply two single phase A.C. induction motors in parallel. The no-load terminal voltage of the generator is 400V. And it has an output resistance of 0.2ohms...

Homework Statement Calculate the work W_{A B} done by the force F using Newton's laws (F=ma, etc), when a particle moves from the point A to the point B along the unit circle. The angle is \theta. No friction. How do you define kinetic energy in polar coordinates?Homework Equations...

Homework Statement I have a motor with a full load output rating of 2.8 kW with an effciency off 70% and at 80% of full load runs with a Power Factor of 0.8 lagging. A second motor has afull load output of 4.2kW with an effciency of 85% and at 80% of full load runs with a PF of 0.75...

Homework Statement I am having difficulty with a question on my Electrical course and the expressing a motor load voltage and current in polar form. The motor is single phase 2.8 KW efficiency 70% and 80% of full load runs with a power factor of 0.8 lagging. Voltage 400v. Express the motor...

Homework Statement ∫ e^(\pix^2) dx, with limits -∞ to ∞ Homework Equations ∫∫ dxdy = ∫∫ rdrdθ The Attempt at a Solution Hi, here's what I've done so far: Introduce a dummy variable y to get ∫∫ e^\pi(x^2 + y^2) dxdy, with limits -∞ to ∞ for both dx and dy...

Homework Statement \int\int of R ( sin( x^2 + y^2) ) dA where the region 4\leq x^2+y^2 \leq 49 Homework Equations not too sure but i know that dy dx = r d(r) d(theta) The Attempt at a Solution i don't understand how to change into polar coordinates in order to integrate. I'm...

Homework Statement Hi guys I have been given a question, write down w* in polar form where w=2< -(pi/3). I can work out the question when it is in cartesian form just not this way, any help woud be great. Homework Equations The Attempt at a Solution

Find the area enclosed by the curve r=(1+Cos\theta),0\leq \theta \leq 2\pi |cos \theta|\leq1 Maximum r =2(1+1)=4 When r=0, 2+2Cos\theta=0 Cos\theta=-1 Key angle=0 \theta=\pi,3/2\pi Area of curve =1/2\intr^2 dtheta

Homework Statement We define the improper integral (over the entire plane R^2) I as a double integral [-inf,inf]x[-inf,inf] of e^-(x^2+y^2)dA as equal to the lim as a-> inf of the double integral under Da of e^-(x^2+y^2)dA where Da is the disk with the radius a and center at the origin...

I'm sure my question is very simple to most of u guys. But I have the following confusion. Let's say we have an AC voltage source in a circuit. In rectangular form it's phasor form is v= -4 - 16 j . I want to write this phasor in polar form. Well, The phasor is in 3rd quadrant of complex...

Homework Statement A satellite is in a circular polar orbit 240 km altitude. When the satellite is over the South Pole the engine is fired to achieve a polar orbit that has apogee directly over the North Pole. After the impulsive burn an observer on the North Pole observes the satellite has...

Homework Statement I want to find the divergence operator in polar coordinates (theta and r). I know how to write this operator in cartesian coordinates. The Attempt at a Solution I let F(F1,F2) be a vector field. I calculated the partial derivatives of F1 and F2 with respect to x...

Homework Statement http://img162.imageshack.us/img162/9831/97118623.jpg Homework Equations The Attempt at a Solution I first drew R, and from the circle equation, I know the radius of the circle is 12.5. Since the region is in the first quadrant, that'll mean that my limits of...

Homework Statement Rewrite by converting to polar coordinates, carefully drawing R. \int^{2}_{0}\int^{\sqrt{2x-x^2}}_{0}\sqrt{x^2+y^2}dydxHomework Equations The Attempt at a Solution I believe I have the inside part of it right. What I did was replace the x^2 and y^2 in \sqrt{x^2+y^2} with...

Evaluate the integral by changing to polar coordinates \int\int arctan(y/x) Given that 0 \leq x \leq 1 and 0 \leq y \leq x Now I've changed the integral to \int\int \theta r dr d\theta Such that 0 \leq \theta \leq \frac{\pi}{2} and 0 \leq r \leq \sqrt{2} And evaluating this...

Homework Statement Use Green's theorem to compute the area of one petal of the 28-leafed rose defined by r = 5sin(14 \theta) Homework Equations A = \frac{1}{2} \int_c{x dy - y dx} \int \int_c{M_x + N_y}dx dy The Attempt at a Solution I'm really more confused about just what to do...

Homework Statement A pendulum consists of a particle of the mass m and a thread of the length l (we don't consider the threads mass). The acceleration caused by gravity is g. Solve the particles displacement and the force caused by the tension in the thread T in a polar coordinate system. The...

Homework Statement I need to integrate the equation shown below in the picture. It is a polar coordinate function with r(double dot) being the acceleration radial and theta(double dot) being angular acceleration. I need to integrate with respect to time, to get equations for r(dot) and r...

Homework Statement how can i convert this : - 2 (cos pai / 4 + i sin pai / 4 ) to Cartesian , Polar and Exponential form ? Homework Equations z = ( a + i b) The Attempt at a Solution r= -2 tan inverse = pai/4 / pai/4 ?? Thank you very much for helping me out

Express -2(cos pai/4+i sin pai/4 ) in Cartesian , Polar and Exponential form ? how can i convert this : - 2 (cos pai / 4 + i sin pai / 4 ) to Cartesian , Polar and Exponential form ? Thank you very much

Homework Statement using only trigonometric identities, derive the differential area element in polar coordinates? any help with this problem or at least a start? Homework Equations i found this so far dA=(dr)(rd θ) The Attempt at a Solution i have tried to figure this one out...

I came across this example on the net : We are integrating over the region that is the area inside of r = 3 + 2 sin θ and outside of r = 2, working in polar coordinates (r,θ). What is the limits of integration for θ? # I already know the answer. But I have no idea how to arrive at the...

Hi there, I am getting confused about how to work this out. I know that to convert cartesian coordinates to spherical coordinates you can use: theta=arccos(z) phi=arcsin(y/sin(theta)) my problem is that I have a list of coordinates, let's call them THETA and PHI. I change them into X,Y,Z...

Any web resources regarding changing the variable of integration from cartesian to polar coordinates that goes beyond the basic : x = r cos theta y = r sin theta r = sq rt (x^2 + y^2)I totally don't get how to find the limits of integration using polar coordinates and my undergrad textbooks...

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 ∫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...

it is the typical pde heat equation in polar coord: \partialu/\partialt = \partial^2u/\partialr^{2} + (1/r) \partialu/\partialr + (1/r^{2}) \partial^2u/\partial\Theta^2 where: - 0 < r < 1 - 0 < \Theta< 2 \Pi - U(1, \Theta, t ) = sin3\Theta - U(r, \Theta, 0 ) = 0 I don't know how...

Homework Statement Hyperbola formula 9x^2 - 4y^2 + 36x + 24y - 36 = 0. Convert to rectangular form, find coordinates of the vertices, find coordinates of the foci, find eccentricity, what is the equation of the conic section in polar coordinates if the pole is taken to be the leftmost focus...

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%...