Questions on polar coordinates, a coordinate system where points are represented by their distance from the origin ($r$) and the angle the line joining the point and the origin makes with the positive horizontal axis ($\theta$).

learn more… | top users | synonyms

1
vote
0answers
51 views

What is a complex number that can't be written in polar form?

What is the cartesian form of a complex number that can't be written in polar form? Why can't it be written in polar form?
2
votes
5answers
46 views

Find the center and radius of polar circle equation [on hold]

Find the radius and center of the circle $$r=2\cos \theta+3\sin \theta$$
0
votes
0answers
21 views

why this formula doesn't work?

L=integral from theta(start) to theta (end) r d(theta )......to find the arc length we usually use L= integral from theta(start) to theta (end) sqrt r^2+(dr/dtheta)^2 dtheta why the first formula ...
0
votes
1answer
18 views

Show that $u(x)=\ln\left(\ln\left(\frac{1}{1+|x|}\right)\right)$ is in $W^{1,n}(U)$, where $U=B(0,1)\subset\mathbb{R}^n$.

The entire problem statement is: Let $n>1$ and let $U=B(0,1)\subset\mathbb{R}^n$. Show that $u:U\to\mathbb{R}$ given by $$u(x)=\ln\left(\ln\left(\frac{1}{1+|x|}\right)\right)$$ is in ...
1
vote
2answers
19 views

Find Cartesian coordinates of polar curve $r =5\sin(\theta) + 5\cos(\theta)$

Polar equation of the form $r = 5\sin(\theta) + 5\cos(\theta)$ The Cartesian equation is of the form $(x-A)^2+(y-B)^2 = R^2$ Find $A,B$, and $R$. Guess: Let $x = R\cos(\theta) + A$ and $y = ...
0
votes
3answers
15 views

How can I calculate angles between objects at the sky?

There is a polar coordinate system which represents the sky from an observer. The elevation angle is 0 to 90 degrees which corresponds to horizon to zenith. The azimuth angle is 0 degrees (north) ...
-1
votes
2answers
44 views

A triangle having coordinates $(a\cos\phi, a \sin\phi) , (a\cos\theta, a\sin\theta) , (a\cos\psi, a \sin\psi)$…

A triangle having coordinates $(a\cos\phi, a \sin\phi) , (a\cos\theta, a\sin\theta) , (a\cos\psi, a \sin\psi)$ having its area $$ \Delta = 2a^2 \sin\frac{\theta - \phi}{2}\sin\frac{\phi ...
1
vote
0answers
13 views

Alpha and Omega Limit Sets in Polar Coordinates [duplicate]

I guess here I am not sure how to get started, I know the definitions: The $ω$-limit sets of points are the set of points that the system of equation approach as time goes to infinity, and the ...
2
votes
1answer
20 views

Use triple to verify that a paraboloid divides a solid in two regions of the same volume, where am I wrong?

Let $S$ be the region over the $xy$ plane and inside the intersection of the cylinder $x^2+y^2=a^2$ and the plane $z=a^2$. I want to verify that the paraboloid $z=x^2+y^2$ divides $S$ into two ...
0
votes
2answers
30 views

Polar coordinates, Differentiation

Can someone clarify this step for me please, "The polar coordinate r satisfies $r^2=x^2+y^2$, so by differentiating with respect to t we get $r\cdot\dot r=x\cdot\dot x+y\cdot\dot y$" I am totally ...
-1
votes
1answer
32 views

Change of Variables Diff Equation Polar [on hold]

(a) Show that the general solution to the differential equation $\frac{dy}{dx}=\frac{x+ay}{ax-y}$ can be written in polar form as $r=k{e^a}^\theta$ . b) for the particular case when a = 1/2 , ...
2
votes
2answers
32 views

Understanding the Jacobian

I was given this problem: Use double integrals to find the area under the curve defined by $r=1+\sin\theta$. We can see that $0\leq\theta\leq2\pi,$ and $0\leq r\leq 1+\sin\theta.$ My question is, ...
0
votes
0answers
32 views

Find the volume of the solid described by $x=x^2+y^2$ and the plane $z=y+2$

I'm trying to use triple integrals to find the volume of the solid described by $x=x^2+y^2$ and the plane $z=y+2$. I already determined that the projections of this solid in the plane $xy$ and $xz$ ...
0
votes
2answers
28 views

Double integral with polar?

I have the following integral : $$\iint\limits_R \operatorname e^{-\frac{x^2+y^2}{2}} \operatorname d\!y \operatorname d\!x $$ Where R is: $$R=\{(x,y):x^2+y^2 \leq 1\}$$ I think I should convert to ...
1
vote
2answers
39 views

Solve double integral

$$ \int_0^2 \int_0^{4-x^2} \frac{xe^{2y}}{4-y} \, dy\, dx $$ I'm stuck with this problem. I think I should change it so I integrate with respect to $dx \, dy$ but I'm not sure. Any help? Thanks
0
votes
1answer
23 views

Solve the double integral

I am calculating: $$ \int\int_R (2ax-x^2-y^2)^{\frac{1}{2}} \, dA$$ Where $R$ is the region determined by the inside of $x^2+y^2-2ax=0$ So far, I tried using polar coordinates, wich turns the ...
0
votes
1answer
13 views

Graphing in Polar Coordinates

I´m currently using polar coordinates to calculate some double and triple integrals. However, I have an small doubt; when you are want to express, lets say, a circle of radius $a$ centered in $(a,0)$ ...
0
votes
0answers
26 views

Limits of Integration in Polar Coordinates

I am in multivariable calculus and learning to do double integrals by switching from Cartesian to Polar coordinates. Substituting for the integrand is easy, the part I find most difficult is ...
0
votes
2answers
25 views

System of equations, limit points

This is a worked out example in my book, but I am having a little trouble understanding it: Consider the system of equations: $$x'=y+x(1-x^2-y^2)$$ $$y'=-x+y(1-x^2-y^2)$$ The orbits and limit sets ...
3
votes
1answer
34 views

Conversion of polar coordinate differential 1-forms to xy-plane

I am new to differential geometry (and StackExchange!) and am having some trouble with the conversion of the polar differential one-forms: $dr$ and $d \theta $. How do I express these in terms of ...
1
vote
1answer
44 views

Integral by polar coordinates

How to calculate the integral $$\int_0^6\int_0^y x\;dx dy$$ using polar coordinates?$$$$I know that $x=R\cos \theta$ and $y=R\sin\theta$ and that the Jacobian is $R$.
0
votes
1answer
17 views

Specific cartesian coordinates of an ellipse

I want to do the following: 1.) Ask user for the vertical and horizontal distances of the ellipse 2.) With this information calculate the circumference 3.) Divide the circumference by the closest ...
4
votes
2answers
51 views

Better substitution calculating integral?

I'm calculating $$ \iint\limits_S \, \left(\frac{1-\frac{x^2}{a^2}-\frac{y^2}{b^2}}{1+\frac{x^2}{a^2}+\frac{y^2}{b^2}} \right)^\frac{1}{2} \, dA$$ with $$S =\left\{ (x, \, y) \in \mathbb{R}^2 : ...
3
votes
2answers
83 views

converting improper double integrals to polar form: what do I do with infinity limits

I need to convert $$ \int_{-\infty}^{\infty}\int_{-\infty}^{\infty}-e^{\frac{x^2+y^2}{5}}dA$$ To polar form. I know $x^2+y^2 = r^2, $ and $dA = rdrd\theta$ But what do I do with the $\infty$ ...
0
votes
2answers
31 views

Need help converting $z = \ln(x^2 + y^2)$ to polar

The full question is this: Volume of a solid in any region R is given by: $$\int\!\!\!\int_Rf(x,y)dydx $$ where, $$f(x,y) = z = \ln(x^2+y^2)$$ and, $$x^2+y^2=r^2$$ There for, $$dydx = ...
1
vote
0answers
19 views

What function has a 3D graph that will look like a spiral into a singularity?

I am trying to draw text spiraling into a black hole, from a more interesting slightly off-orthogonal viewpoint. I think a function that defines a black hole/singularity surface might look something ...
0
votes
0answers
18 views

Double Integral Mistake with Parametric Equation

I'm trying to figure out the mass of an object bounded by $y=0$ and $y=\sqrt{1-x^2}$ the density at a given point is proportional to its distance from the origin; $\rho(x,y) = kxy$. So I set it up ...
1
vote
0answers
14 views

Convert geodetic coordinates to cartesian coordinates

I am working on some simulation software that will represent a number of entities in a defined geographic area in the world. The part of the software that I am currently working on is to implement ...
1
vote
2answers
22 views

solve polar coordinate integral

Evaluate $$\int_0^R\int_0^\sqrt{R^2-x^2} e^{-(x^2+y^2)} \,dy\,dx$$ using polar coordinates. My answer is $-\frac{1}{2}R(e^{-R^2+x^2}-1)$ but I want to confirm if that's correct And also, when I ...
1
vote
0answers
34 views

Find arc centerpoint(x,y) with start(x,y) and end(x,y) in a conical helix

Im trying to script drawing of a conical helix in 3D software, and are stuck at the last arc when its not a full 180 degree arc. I know(calculate) the arc startpoint and endpoint, but how do I find ...
1
vote
1answer
21 views

Cartesian to Polar coordinates where alpha is real parameter

I want to convert the following equation in Cartesian form to Polar: $$-y(1+\alpha+x)+x(1-x^2-y^2)$$ so $x = r\cos(\theta)$ and $y = r\sin(\theta)$ I can get this far: ...
0
votes
1answer
24 views

Is it possible to write all of the functions in terms of polar form?

Is it possible to write all functions in terms of polar form? For example, the equation of the circle with radius one can be written like $r=1$ I'm wondering whether reform the equations of all curves ...
0
votes
2answers
30 views

Finding the Equation of a Tangent Line to a Polar Curve

Find the equation of the tangent line to the polar curve: $r=3-3\sin\theta$ at $\theta=\frac{3\pi}{4}$ I have the equation: $$\frac{dy}{dx} ...
0
votes
1answer
15 views

Tangent Line of Polar Curve

i start by changing polar coords into x and y and then find the derivatives to get the slope. $$x=(3-3\sin\theta)\cos\theta $$ $$x=3\cos\theta -3\cos\theta \sin\theta $$ and took $x'=(-3\sin\theta ...
0
votes
0answers
16 views

How to make a polar symmetry proof

I have an exercise that ask for a symmetry proof of the function: $$r=\sin(3\theta)$$ and $$r^2=2\cos(2\theta)$$ But i really dont know what they ask and what to do.
1
vote
1answer
50 views

Transform second order partial derivatives into polar coordinates

I have the following question: Let $u(x, y)$ be a function with continuous second order partial derivatives. Use the chain rule to transform the expression: $$ x^2\frac{\partial^2u}{\partial ...
2
votes
1answer
32 views

Changing to polar form for Green's Theorem

In my text given the integral $\int_{\partial{D}} xy\,dx$, and that $$\int_{\partial{D}} xy\,dx=-\int\int_{D}x\,dx\,dy = - \int\int r\cos \theta\,r\,dr\,d\theta$$ I'm not really understanding the ...
0
votes
4answers
41 views

Limit using polar coordinates?

$$\lim_{(x,y) \to (0,0)} \frac{x y^2}{(3x^2 + 4x^2)}$$ How would one calculate above "using polar coordinates"? It was mentioned during class shortly, but we won't be introduced to this until next ...
0
votes
1answer
19 views

How to find the limits of integration to get the area for a loop of a lemniscate?

I know how to integrate the squared radius to get the equation that'll give me the area, like such for a lemniscate with $r^2=8\sin(2\theta)$ : $$1/2\int 8sin(2\theta) = 4 \int \sin(2\theta) = 4 * ...
0
votes
2answers
25 views

Divergence of vector in spherical coordinates

How should I calculate the divergence for $$\vec{V}=\frac {\vec{r}}{r^2}$$ Is it possible to convert it from spherical coordinates to cartesian?
0
votes
1answer
44 views

Function in Polar Coordinates

Let $f,g:I\to\mathbb{R}$ be two function in $C^{k}(I)$, with the property that $f^2(t)+g^2(t)=1, \ \forall\ t\in I$. Is there a function $\theta: I\to\mathbb{R}$, $\theta\in C^{k}(I)$, such that: ...
0
votes
1answer
21 views

What is the cartesian equation of $r = 4 + \frac{\sin(\theta)}{2}?$

This is extremely similar to this question, but as there is no r next to the constant 1, when I multiply everything by r I'm going to end up with: $r^2 = 4r + r\frac{\sin(\theta)}{2}$ And I don't ...
1
vote
1answer
18 views

Double integral in cylindrical coordinates

I'm having trouble with a double integral problem in cylindrical coordinates. I'm sure the answer is staring me in the face, but I'm missing something. In the multivariable version of the Community ...
-1
votes
1answer
48 views

Double Integral to Polar Coordinates

Evaluate $$\int_{0}^{2}\int_{0}^{\sqrt{2x-x^2}} \sqrt{x^2+y^2}dydx$$ by converting to polar coordinates. I sketch the region which is a half circle from $0$ to $2$ on the $x$-axis and $0$ to $1$ ...
0
votes
1answer
21 views

Graphing A Polar Equation

So, I encountered a question r = -|sinø|. So, I thought the polar graph would look like (2) but it actually looks like (3) and I don't understand why. Can someone explain it to me? I've attached a ...
0
votes
0answers
34 views

TI-83 gets a simple convertion to polar form wrong

I am trying to do the equation $-1-i$ converted to Polar form on the format e^i The answer (according to my own computations) should be $$ \sqrt2e^{i5\pi/4} $$ While the calculator says it is $$ ...
1
vote
2answers
66 views

In polar coordinates, can r be negative?

I'm getting different answers for this. Many websites say that when you get a negative value of r, you flip the coordinate 180 degrees across the pole. However my teacher says that you cannot have a ...
1
vote
1answer
23 views

Arc length of a polar curve in terms of theta

Is there an equation for such? I know that there is an equation for such in terms of r, but I must calculate the length of $tan(\theta) = 3/5$ (cartesian equivalent: $y = 3/5x$) from r = 0 to 1.457. ...
0
votes
2answers
12 views

Points of intersection for two polar equations question

Why is it that when I try to find the points of intersection for $r=2$ and $r=4*\cos(2\theta)$, I only get the $\theta$ where the reference angle is $\pi/6$? There is clearly another solution between ...
0
votes
2answers
41 views

How can I solve these two tough integrals?

\begin{equation*} J_{1} = \int_{0}^{\sqrt{{\pi}/{6}}} \int_{y}^{\sqrt{{\pi}/{6}}} \cos{(x^2)}\,dx\,dy \end{equation*} \begin{equation*} J_{2} = \int\int_{E}\int z e^{(x^2+y^2)} + xe^{x^8}\,dV, ...