Polar Definition and 1000 Threads

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 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...

Homework Statement Find the length of r = theta^(2) for 0<=theta<=pi Homework Equations Arc length s = antiderivative of sq rt (f (theta)^(2) + f (derivative theta)^(2)) The Attempt at a Solution I have worked my way to the antiderivative of sq rt (theta^(4) + 4(theta)^(2)) but I'm...

Homework Statement Convert to an equation in polar coordinates y = x^(2) Homework Equations x = r cos (theta) , y = r sin (theta) , tan (theta) = y/x The Attempt at a Solution Here is my work so far: y=x^(2) so r sin (theta) = (r cos (theta))^2 and r sin (theta) = r^(2)...

why no change of variable to polar coordinates inside multi-loop integral ?? given a mul,ti-loop integral \int d^{4}k_{1} \int d^{4}k_{2}....\int d^{4}k_{n}f(k_{1} , k_{2},...,k_{n}) which can be considered a 4n integral for integer n , my question is why can just this be evaluated by...

I'm doing work on polar coordinates in double integrals. Could someone explain why when circles aren't centered on the origin the angle only varies from (if it is translated above the origin) 0 to pi. I thought the angle was supposed to be the angle in the circle, so if its a full circle then 0...

I had a question in a lab about which elements are least likely to form polar covalent bonds with hydrogen. From what I understand, what governs how polar a bond is, is the electronegativity of the element. The answer said that Carbon was the one which was least likely to form the bond, but...

Hi guys, I was trying to sketch a polar curve but my curve was different from the curve on maple(I plotted the same curve on maple). Homework Statement Here is the whole question, I am using t as theta. The hyperbolic spiral is described by the equation rt=a whenever t>0,where a is a...

Equation of tangent line (rec. form) to a polar curve! Homework Statement Quesiton: Find the rectangular form of the equation of the tangent line to the polar curve r=cos^3(theta) at the point corresponding to theta=pi/4 Homework Equations The Attempt at a Solution How to...

Homework Statement I'm trying to help a friend with these two questions, but given that I haven't studied this material in over a decade, it's one of the topics I cannot recall at all. Convert the following from rectangular to polar coordinates: (a) x2 + y2 = x (b) y2 = 2x...

Homework Statement find the area inside both of the curves r = 4 cos@ r = 2+2cos@ @ = theta Homework Equations ------- The Attempt at a Solution i will say 4cos@ = 2+2cos@ to find the intersection points 4cos@ = 2+2cos@ 2cos@ = 2 cos@ = 1 @ = 0 ! I need the other points!

In the polar formula for arc length, ds^{2}=dr^{2}+r^{2}d{\theta}^{2}, what is the exact meaning of the r^2 term multiplying d{\theta}^2? Is it an initial distance from the origin? A final distance from the origin? The change in r from point a to point b? This baffles me to no end and nothing...

Homework Statement Let C be the curve whose equation is given by: 4x^2+18y-20=9y^2+16x+9 Identify and sketch the curve C and if possible give its center, directrix, foci, vertices, and endpoints on the minor axis. Homework Equations I have learned parabola, hyperbola and elispes (these are...

Homework Statement I have some questions want to be answered. 1. For rose, I believe there are two kinds, dealing with even peals and odd peals. My math professor confused himself in the lecture and could not tell us the right identification. The book is also helpless. For example, the form...

Homework Statement let r = sin(t)+ cos(t) sketch the graph Homework Equations The Attempt at a Solution i really don't know how to start this off. i know some working should be done in order to sketch it but what?

I can't seem to get the correct answer. I rechecked my calculations but no luck. Any help is appreciated. Thanks. Homework Statement Find the area inside the larger loop and outside the smaller loop of the limacon below. r = sqrt(3)/2 + cos(theta) Homework Equations A = (integral...

My question here is do I have the correct limits of integration? At first I thought it would be from pi/10 to 3pi/10 but I have a feeling that those are incorrect. Homework Statement Find the area of one petal of the polar function r(x) = cos(5x) Homework Equations...

Homework Statement Find the area of the region enclosed by one loop of the curve. r = sin(10θ) I can't seem to get the correct answer...I checked every step. I was not sure what to integrate from but the polar graph of sin(10θ) should be similar to polar graph of sin(2θ). From pi/2 to 0...

can someone explain to me why my teacher divided the area into two? I=\int1,0\int(2x-x^2)^.5,0 1/(x^2+y^2)^.5dydx ugggggh i tried to use the latex... anyway... he used the polar coordinate to do this. once he turned it into polar coordinate, he divided the area into 2 bounded by (pi/4 - o...

Homework Statement (5∠2.214)/(√5∠-1.107) ive gotten this far in a problem(thats the answer but i need to simplify).. all i need to know is how to divide the angles? Homework Equations The Attempt at a Solution

I can't really understand something in spherical and cylinder coordinates let me start with polar coordinates first if we have for example x^2 + y^2 = 4 this is a circle with center (0,0) and radius 2 in polar coordinates x and y will be x = rcosφ y = rsinφ 0<=r<=2 0<=φ<=2π here φ is from 0...

Homework Statement Find the slope of the tangent line to the given polar curve at the point specified by the value of θ. r = 9sin(θ) θ = pi/6 Homework Equations dy/dx = (dy/dθ) / (dx/dθ) x=rcosθ y=rsinθ (sinx)^2 = (1/2)(1-cos2x) (cosx)^2 = (1/2)(1+cos2x) 2sinxcosx = sin(2x) The Attempt at...