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 ($\theta$).
4
votes
1answer
31 views
Polar coordinations - problem with r and $\theta$
let's take a look on Archimedean spiral.
the polar equation is $r = \theta$. click here to look.
but $\tan (\theta) = y/x$ and $r = \sqrt{x^2+y^2}$,
so $r = \theta \rightarrow \tan(\sqrt{x^2+y^2}) ...
0
votes
1answer
19 views
Determining the correct upper bound for an integral in polar coordinates
This seems super easy. But i am just a little bit stuck here. Haven't done much calculus recently. Can someone help me out real quick?
Thank you in advance!
2
votes
2answers
72 views
+50
Integration of radial functions?
Let $f(|x|)$ be a integrable radial function in $\mathbb{R}^n$ ($|\cdot|$ denotes the euclidean norm as in convention). The following identity is used to simplify computations
...
1
vote
1answer
45 views
How did theta become equal to 3pi/4 here?
How did theta become equal to 3π/4 in this particular example?
Find a set of polar coordinates (r,θ) of the cartesian point (-4,4)
such that -2π ≤ θ ≤ 2π and
a. r > 0 and θ > 0 b. ...
1
vote
1answer
46 views
Inaccuracy in numerical calculation of arclength of part of an ellipse
I am trying to numerically calculate the arclength of part of an ellipse according to:
$$ L = \int_0^{\phi_s}\sqrt{r^2+\left(\frac{dr}{d\phi}\right)^2} d\phi $$
where $r$ is defined as:
$$ ...
1
vote
1answer
36 views
Finding area between two polar curves using double integrals
I have a homework question that is asking me to find the area that lies:
Inside the curve $r=2+cos(2\theta)$
But outside the curve $r=2+sin(\theta)$
I think I'm supposed to be using a double ...
3
votes
3answers
63 views
Trying to understand the meaning of symmetry
The picture below is the solution to the following problem as presented in my book:
Find the area of the region that lies inside both curves $$r = 8 + \cos \theta \\r = 8 − \cos θ$$
According to ...
-1
votes
1answer
58 views
Moment of inertia of a circle
A wire has the shape of the circle $x^2+y^2=a^2$. Determine the moment of inertia about a diameter if the density at $(x,y)$ is $|x|+|y|$
Thank you
4
votes
1answer
105 views
Mexican Hat wavelet in polar coordinates
I'm interested in wavelet framework for polar coordinates.
In the paper of Hou&Qin (2012) was proposed a general method for definition of MH wavelets on a certain manifold. In short, first we ...
2
votes
2answers
87 views
Find Cartesian equation of $r=\theta$
I solved this problem, but I'm not sure my answer is correct as it seems very complex (compared to the polar equation). Did I make some mistake along the way or is it the right solution?
$$r=\theta$$
...
0
votes
2answers
50 views
Don't understand how to use jacobian for transformation of coordinates
Hello. I fail to understand why the Jacobian matrix is used to transform Cartesian coordinates to polar coordinates.
If I'm not misunderstanding, it is assumed that the matrix ...
2
votes
1answer
56 views
Find a Cartesian equation of $r = 4\cos\theta$
I was able to figure the substitutions inside the equation, but I'm stuck with the equation's manipulation that will give me the solution. What would be my next step?
$$r = 4\cos\theta$$
$$r^2 = ...
3
votes
0answers
54 views
Parametrization of a curve in polar coordinates
I'm trying to change this parametrics equations to polar coordinates
$$ X(t) = 2\cos(t) - \sin(2t) \\
Y(t) = 2\sin(t) - \cos(2t) $$
What i tryed to do was raise the two equations squared, sum ...
1
vote
1answer
31 views
Line integral of $F = r \times k$ on hemisphere
Exam revision -
Verify Stokes theorem directly by explicit calculation of the surface and line integrals for the hemisphere $r=c$, with $z \geq 0$, where $F = r \times k$ and $k$ is the unit vector ...
1
vote
1answer
60 views
Polar Coordinates: Dividing by the variable “r.”
Evaluate the iterated integral by converting to polar coordinates:
$\large \int^2_0 \int^{\sqrt{2x-x^2}}_0 xy~dy~dx$
I successfully completed most of the problem; however, I had difficulty ...
0
votes
0answers
43 views
Which complex number cannot be written in polar form?
I'm really confused by this question. Is there such a number?
0
votes
1answer
75 views
How does one interpolate between polar coordinates?
I'm finding that when I try to use the standard methods of interpolation in polar space, the result is not what I would expect. For example, when interpolating between the following polar coordinates:
...
0
votes
2answers
35 views
Finding the centroid of a polar curve
The curve is $r = e^{-b\theta}$ where $b > 0$ and $θ \in [0, \infty)$.
I got that the arc length is $\frac{\sqrt{b^2 + 1}}{b}$ (is this correct?), but computing the centroid $(x, y)$ looks awful. ...
3
votes
1answer
167 views
How to calculate the area between 2 polar curves: $r=\frac{4}{2}-\sin\theta$ and $r=3\sin\theta$?
How to calculate the area between 2 polar curves: $r=2-\sin\theta$ and $r=3\sin\theta$?
I know that one curve is a limaçon and the other is a circle. I have them drawn out as well, my only question ...
1
vote
2answers
64 views
Integration, polar coordinates
My question is general rather than specific.If a problem requires to find the area of a figure bounded by a curve given in polar coordinates,how do we find the limits of integration analytically ...
3
votes
1answer
38 views
polar coordinates ..question about the answer from the solution manual
Im trying to figure out but for some reason I dont know how to...could someone please tell me how did they get this answer from the solution manual....they skipped steps so I have no idea
1
vote
1answer
44 views
Express in Rectangular Form
a) $(-1+i)^{-i}$
so I know that the answer is $9.92-3.58i$. My track getting there is off.
I know that $x=-1$ and $y=1$, so $r = \sqrt{2}$, also that $\displaystyle \theta=-\frac{pi}{4}$.
I've ...
2
votes
0answers
30 views
Pure differential equation whose solution is a siluroid?
I am trying to find a differential equation for the siluroid that DOES NOT contain explicitly $\theta$, $\sin\theta$, or $\cos\theta$, but only $\rho$, $\dot\rho$, $\ddot\rho$. The siluroid equation ...
0
votes
0answers
32 views
Polar fourier transform
I need help please.
I have a 2D signal : sg=sin(x+y). to represent it in 2D i use meshgrid: [xx,yy]=meshgrid(x,y) and i represented with surf(xx,yy,sg).
Now i want to transform my signal in polar ...
2
votes
4answers
73 views
Converting x^2 + 6y - 9 = 0 to polar
Hi I'm trying to solve this problem but am having difficulty removing the remaining r. I have tried http://i.imgur.com/iJk9b2g.jpg but cannot get an answer
Any help is appreciated
1
vote
1answer
46 views
Polar coordinate
Let $f(x,y)$ be a differntiable function in $\mathbb{R}^2$ so that
$f_x(x,y)y=f_y(x,y)x$ for all $(x,y)\in\mathbb{R}^2$.
Find $g(r)$ so that $g(\sqrt{x^2+y^2})=f(x,y)$ and $g$ is differentiable in ...
2
votes
1answer
53 views
evaluation of double order integral using polar co-ordinates
When evaluating double integral using polar co-ordinates,
does the order of $dr ~ d\theta$ make any difference?
Suppose,
$$\int_0^{\pi/4}\int_0^{\sin\theta} r^2 dr d\theta$$
...
1
vote
1answer
61 views
How to calculate a double integral over a triangle by transforming to polair coordinates & by using a transformation
Let T be the triangel with vetrices $( 0,0 ) , ( 1,0 )\mbox{ and } ( 0,1 ) $. Evaluate the integral :
$$
\iint_D e^{\frac{y-x}{y+x}}
$$
a) by transforming to polar coordinates
b) by using the ...
1
vote
1answer
108 views
triple integral - ecliptic coordinate
I need to find the $V$ by triple integral.
the limits from up is (1) - ecliptic cone.
and from dwon - (2) - elepsoide.
$$(1) \ \ \ \ z=-\sqrt{3x^2+5y^2}$$
$$(2) \ \ \ \ {3 \over 10}x^2+5y^2+{z^2 ...
1
vote
0answers
47 views
gradient of an axis symmetric vector field in cylindical coordiantes
I am trying to calculate with a general approach the gradient of an axis symmetric vector field in cylindrical coordinates and then express it in cartesian coordinates.
First I write my vector ...
0
votes
1answer
467 views
Find the area of the Rose's petal.
If a Rose leaf is described by the equation $r = \sin 3\theta$, find the area of one petal.
0
votes
2answers
19 views
Polar coordinates that uses $\frac { 1 }{ Z_1 }$
I am doing polar coordinates, and I am stuck when my book asks to do $\frac { 1 }{ Z_1 }$. I have no problems with $\frac { Z_1 }{ Z_2 }$ and $Z_1Z_2$. Here is the values for $Z_1$ I'm not so much ...
1
vote
1answer
59 views
What happens to a line in polar coordinates when orgin is moved and rotated in cartesian coordinates?
Let's say we have an Archimedean spiral in Cartesian coordinates. This corresponds to a line in polar system (i.e. $r=a\theta+b$).
Now if I move the origin of the Cartesian coordinates system to ...
1
vote
2answers
79 views
Coordinate system conversion: what it is called what I'm doing?
I want to do a simple coordinate transformation and would like to know what is the rigorous way to describe this mathematically in order to be able to search for algorithms for more complex ...
0
votes
1answer
49 views
Polar form $\frac{dy}{dx}$
Trying to find the derivative $\dfrac{dy}{dx}$ in polar form, where:
$$x=r\cos\theta \,\text{ and } \, y=r\sin\theta$$
Seems like the common approach (on Wikipedia and other sites) is to assume that ...
0
votes
2answers
87 views
What is the inverse $z^{-1}(z)$ of $z(\varphi)=e^{i\varphi}$ with $\varphi\in\Bbb N_0$?
Suppose I am given a complex number $z=x+iy\in\Bbb C$, with $\left|z\right|=1$, and I am told that $z=e^{i\varphi}$ for some integer $\varphi\in\Bbb N_0$ (the value of which is not given to me).
How ...
1
vote
1answer
934 views
Ellipse in polar coordinates
I think Wikipedia's polar coordinate elliptical equation isn't correct. Here is my explanation: Imagine constants $a$ and $b$ in this format -
Where $2a$ is the total height of the ellipse and $2b$ ...
0
votes
0answers
66 views
How to solve following non-linear differential equation?
Let's have an equation
$$
\left(\frac{\partial f}{\partial r}\right)^{2} + \frac{1}{r^{2}}\left(\frac{\partial f}{\partial \varphi}\right)^{2} = g(r).
$$
How to solve it?
0
votes
1answer
31 views
Qualitative analysis of an ordinary differential equation in polar coordinates
I want to draw the integral curves of the differential equation in polar coordinates $(\theta, \rho)$
$\frac{d\rho}{d\theta}= \rho^3-6\rho^2+8\rho$
At first I thought it would suffice to analyse ...
2
votes
1answer
112 views
Really Stuck on Partial derivatives question
Ok so im really stuck on a question. It goes:
Consider $$u(x,y) = xy \frac {x^2-y^2}{x^2+y^2} $$ for $(x,y)$ $ \neq $ $(0,0)$ and $u(0,0) = 0$.
calculate $\frac{\partial u} {\partial x} (x,y)$ and ...
1
vote
1answer
41 views
Polar coordinates parameters
Sketch in the same diagram the curves with polar equations $r=2a\cos\theta$ and $2r(1+\cos\theta)=3a$ and find the polar coordinates of their points of intersection. What is the polar equation of ...
0
votes
0answers
72 views
How to remember symmetry tests for polar graphs?
Polar $(r , -\theta)$ & $(-r, \pi - \theta)$
Pole $(-r, \theta)$ & $(r, \pi + \theta)$
$\frac{\pi}{2} (-r, \theta)$ & $(r, \pi - \theta)$
1
vote
3answers
111 views
Converting $x^2 + 6y - 9 = 0$ to polar.
So far I got here
\begin{align}
(r\cos\phi)^2 & + 6 r \sin\phi- 9 = 0\\
(r\cos\phi)^2 & = 9 - 6r \sin\phi
\end{align}
2
votes
1answer
51 views
Converting polar to cartesian?
So far I got
\begin{align}
r & = 7 / (4 - 2 \cos\theta) \\
r (4 & - 2\cos\theta) = 7 \\
r (4 & - 2( x / r ) ) = 7
\end{align}
I apologize in advance for the bad formatting.
2
votes
2answers
76 views
Convert $ x^2 - y^2 -2x = 0$ to polar?
So far I got
$$r^2(\cos^2{\phi} - \sin^2{\phi}) -2 r\cos{\phi} = 0$$
$$r^2 \cos{(2\phi)} -2 r \cos{\phi} = 0$$
2
votes
1answer
335 views
Double integral area : how to find the curve equation
I have the following equation
$$(x+y)^{4} = ax^{2}y$$
I need to find the area limited by the equation above. I know I have to transform x and y in polar coordinates:
$$\begin{align*}
&x = ...
0
votes
3answers
86 views
Cartesian and Polar Coordinate
I should give the Cartesian Coordinates $(x,y)\in \mathbb{R\times R}$ and Polar Coordinates $(r,\varphi)\in R^+\times [0,2\pi)$ of the following Complex Numbers:
a) $z_{1}=-i$
b) $z_{2}=\sqrt{3}+i$
...
1
vote
2answers
77 views
Diff eq. transformation polar coordinates
I have $(x',y')=(x-y-x(x^2+y^2)+\frac{xy}{\sqrt{x^2+y^2}},x+y-y(x^2+y^2)-\frac{x^2}{\sqrt{x^2+y^2}} )$
Now I want to use polar coordinates $(x,y)=(r\cos(t),r\sin(t))$ to get ...
0
votes
1answer
160 views
Converting to polar form
Write each of the given numbers in the polar form $re^{i\theta}$.
a.) $\frac{1-i}{3}$
b.) $-8\pi (1+\sqrt 3 i)$
For a, I got:
r = $\frac{\sqrt 2}{3}$ and $e^{i7\pi /2}$ since ...
2
votes
0answers
179 views
Parametrization of square to calculate Dot-product in line-integrals and area-integrals, electric field from $\frac{dB}{dt}$?
I am calculating 3A of Tfy-0.1064 in Aalto University. I realized here that I am misunderstanding something in vector calculus: the thing market in green particularly.
I know
$$\nabla\times E= ...
