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
votes
0answers
12 views

coordinate geometry passage problems [on hold]

Passage $1)$ Let $A( 0, B)$ , $B ( -2 , 0)$ and $C (1 ,1)$ be vertices of a triangle then $Q1)$ Angle $A$ of triangle $ABC$ will be obtuse if $B$ lies in that is the range of $B$ is $a)$ $( -1, ...
0
votes
2answers
20 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
41 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: ...
1
vote
0answers
20 views

Differentiation in polar coordinates at $r=0$; question concerning Theorem 5.7 of Stein and Shakarchi Vol. I

This question arose while I was reading Theorem 5.7 of Stein and Shakarchi's Introduction to Fourier Analysis. It says (in part) Let $f$ be an integrable function defined on the unit circle. Then ...
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 ...
0
votes
0answers
17 views

How to draw an arc with varying thickness [closed]

Arc with various thickness in detail I need to draw an arc in android with varying thickness, as represented in the below image, Is it possible to draw an arc and clip it? as the arc can be ...
1
vote
1answer
16 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
44 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
20 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
33 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
59 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
22 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, ...
2
votes
3answers
213 views

Polar coordinates confusion

This seems to be very easy, however I cannot understand, where I am mistaking. Here's the integral to be computed: $$\iint_Dx^2+y^2dydx$$ with $D:=\left\{(x,y)\in \mathbb{R}^2:x \ge0, \; ...
1
vote
2answers
23 views

Transforming a cartesian equation to a polar one when it has different x and y denominators?

$$\frac{x^2}{9}+\frac{y^2}{16}=1$$ Needs to be replaced with an equivalent polar equation. I'm sure the identity I'll have to use will be $$x^2+y^2=r^2$$ though other options are: $x=rcos\theta$ ...
0
votes
1answer
47 views

How may I use this C loop to solve that integral?

Let C be the curve of polar equation $r = 2cos^2(\theta)$ and D the area bounded by the loop C which is situated in the half-plane $x \ge 0$ region. How may I calculate the D's area and use it to ...
1
vote
1answer
24 views

How to describe the region inside a sphere and below a cone in cylindrical and spherical coordinates?

If E is the region of space located inside the sphere $x^2 + y^2 + z^2 = 4$ and below the cone $z = \sqrt{3x^2 + 3y^2}$ How may I describe E in cylindrical and spherical coordinates? And how may I ...
0
votes
0answers
37 views

Fourier inversion of an infinitely divisible multivariate gamma measure represented in polar form.

Let $\mathbb{S}^{N-1}$ be the unit sphere in $\mathbb{R}^N$ under the Euclidean norm $||\cdot||$. Let $\mu$ be an infinitely divisible Borel measure. If there exists a finite measure $\alpha$ on ...
0
votes
1answer
19 views

Area of region in polar coordinates

I have to verify a point: I'm supposed to find the area of the region given in polar coordinates $$\sec{\theta}\le r\le 2\cos{\theta}$$ I plotted the curves of $\sec{\theta}$ and $2\cos{\theta}$ ...
0
votes
0answers
9 views

Finding Polar Components by Raising/Lowering Indices

This is (I think) a simple question—I'm just making sure everything's correct: I'm given a vector field, $v^a$, which has constant Cartesian components $v^x = 0$ and $v^y = 1$. I'd like to find its ...
1
vote
1answer
50 views

Express partial derivatives of second order (and the Laplacian) in polar coordinates

$z=f(x,y)$ where $x=rcosθ$ and $y=rsinθ$ Find $ \frac{\partial z}{\partial x}$ and $ \frac{\partial^2 z}{\partial x^2}$ I'm having big troubles with using chain rule, in particularly the second ...
0
votes
2answers
72 views

for $z,w\in\mathbb{C}$, $\sqrt{zw} = \sqrt{z}\sqrt{w}$?

for $z,w\in\mathbb{C}$, $\sqrt{zw} = \sqrt{z}\sqrt{w}$ I started by writing $z$ and $w$ in polar coordinates, and writing it out, giving another form for the question: $$ \begin{align} y &= ...
1
vote
1answer
19 views

Product rule trig

This was given as a solution to a question and I've tried working it out but can never get the same answer. Here $x=rcosϕ$ and $y=rsinϕ$ It's mostly the first 2 lines I don't understand. Wouldn't ...
0
votes
0answers
16 views

How to visualize a vector from its components (in spherical coordinates)

Let $$\mathbf{v} = A (1 + \cos \theta) \cos \phi \mathbf{\hat{u}}_{\theta} + A (1 + \cos \theta) \sin \phi \mathbf{\hat{u}}_{\phi}$$ be a vector; $\mathbf{\hat{u}}_{\theta}$ and ...
0
votes
0answers
24 views

Lagrangian transformed to polar-coordinates

I recently came across the following variational question: Transform the Lagrangian... $ L(t,x,\dot{x}) = \sqrt{(t^2+x^2)(1+\dot{x}^2)} $ ... to polar coordinates so as to show that the extremals ...
0
votes
1answer
20 views

Show a polar function's diffrentiability

I need to show that $f(r,\theta)=r\sin(2\theta)\ r>0$ is differentiable at each point in its domain, and also decide whether it's $C^1$ or not. How should I approach this?
1
vote
3answers
47 views

Are we really ever plotting in polar coordinates?

Is it true that when we plot in polar coordinates, we are still actually plotting in the x-y coordinate system? Wouldn't plotting in the polar coordinate system really be plotting with $\theta $ and $ ...
1
vote
1answer
36 views

How is $r(\theta) = \sin \frac\theta2$ symmetric about the x-axis?

I understand how it is symmetric about the $y$-axis. because $r(-\theta) = \sin \left(-\frac\theta2\right)=-\sin \left(\frac\theta2\right)=-r(\theta)$ But how is it symmetric about $x$-axis?
1
vote
1answer
25 views

Symmetry of polar equations

In your opinion how to show symmetry in polar equations without graphing. i thought of these methods :- converting to cartesian then test . check the period of the function . please help me any ...
0
votes
1answer
29 views

Set up triple integral for volume (cylindrical coordinates)

I am given the following question Let $D$ be the region in $\mathbb{R}^3$ that lies within $x^2 + y^2 =4$, underneath the surface $z= 4- x^2 - y^2$ and above the surface $z=- \sqrt{9-x^2 - y^2}$ ...
2
votes
3answers
69 views

How to integrate $\frac{y^2-x^2}{(y^2+x^2)^2}$ with respect to $y$?

In dealing with the integration, $$\int\frac{y^2-x^2}{(y^2+x^2)^2}dy$$ I have tried to transform it to polar form, which yields $$\int\frac{\sin^2\theta-\cos^2\theta}{r^2}d(r\cos\theta)$$ But, what ...
0
votes
0answers
25 views

area of the region bounded by two circles

The two circles in polar expressions are: r=sqrt(3)sin(\alpha), and r=3cos(\alpha). I got the answer to be (1/2)integral(from 0 to pi/3) (3cos(\alpha)^2) d(\alpha) + (1/2)integral (from pi/3 to pi/2) ...
0
votes
0answers
28 views

Why aren't polar coordinates global?

Using polar coordinates, why cant we use one coordinate neighbourhood to cover $\mathbb{R}^2$? Can't every point in $\mathbb{R}^2$ can be described by its distance from the origin and its angle from ...
3
votes
1answer
96 views

Two ways to evaluate $\int (\Delta u) v d\Omega$, two different results

I would like to evaluate the integral $\int (\Delta u) v d\Omega$, where the domain $\Omega$ is a cylinder. On the boundaries, either the normal derivative $\partial_n u$ is zero or $v$ is zero. An ...
-2
votes
2answers
51 views

seemingly simple question about polar coordinates

I was recently looking at a problem that looked like this: Let $x = rcos(t)$ and $y = rsin(t)$. Assuming that x is held constant, what is $\frac{\partial t}{\partial r}$? Apparently the correct ...
0
votes
0answers
16 views

Comparison of Parametric and Polar Equations

Having been introduced to parametric equations, I cannot help but question the similarities between parametrized functions and polar functions. A parametric circle is defined by the following: ...
1
vote
2answers
67 views

Evans 's PDE proof

Again, I got stuck. Please help me to understand the following: What is the meaning when you change from integration over the Ball B(x,r) to the surface integration dB(x,s), with another integral ...
0
votes
1answer
20 views

Error with mixed derivatives during derivation of Laplacian in polar coordinates

It can be shown that, if $f:\mathbb{R}^2\to\mathbb{R}$ is a smooth function and the Cartesian and polar coordinates are related by $$ x = \rho\cos\phi\\ y = \rho\sin\phi $$ that $\partial f/\partial ...
0
votes
0answers
26 views

How to translate the polar curves up/down and right/left without referring to Cartesian equations?

If I have a polar equation $r(\theta)$, how can I translate it up/down and right/left? We can do this by converting the equations into Cartesian equations and do the translations we want and then ...
2
votes
2answers
120 views

Plotting a polar curve

The question is, to generate a polar graph using a graphing utility, and to choose parameter interval so that the complete graph is generated. $$r=\cos\frac{\theta}{5}$$ To find such an interval, we ...
0
votes
0answers
22 views

Finding the intersection of 2 coordinates in spherical coordinate system

Sorry in advance for messing up any math term or being confusing. I have the following data: lat1, lon1, alt1, v1, h1 and ...
1
vote
2answers
84 views

Show that the parameterized curve is a periodic solution to the system of nonlinear equations

First I tried to convert the system to polar coordinates. This only made things worse (unless I made some idiotic mistake). Can I plug in the given ellipse (rectangular coordinates) into the ...
0
votes
1answer
29 views

why is theta in a restricted interval? (Polar coordinates)

What is the polar equation of the circle of radius 1 whose centre lies at the cartesian point (1,0)? So I got the correct answer of r=2cos(θ) But then is says theta is in the interval (-π/2)≤θ≤(π/2) ...
1
vote
3answers
38 views

Is there any way to express $\theta=c$ as some function of $r$?

I recently found this: Desmos Graphing calculator. I tried to plot the equation $\theta=45$ but it gave me an error: Sorry, you can't graph $\theta$ as a function of anything yet. So I started ...
9
votes
3answers
163 views

Is Adobe Acrobat's icon a special function?

It looks like a function in polar coordinates. Is it a special function ?
0
votes
2answers
48 views

Intersection of circle and ellipse

I'm looking for the points of intersection of a circle $x^2 + y^2 = r^2$ ($r$ is known, origin is $(0,0)$) and an ellipse $(x - x_0)^2 / a^2 + (y-y_0)^2 / b^2 = 1$ ($a,b,x_0,y_0$ are known). ...
1
vote
0answers
17 views

Solid angle subtended in latitude-longitude maps

I need to scale a latitude-longitude map with the solid-angle each "pixel" subtend. How can I obtain the said solid angle starting from the $\phi$ and $\theta$ angles? Thank you very much
1
vote
2answers
33 views

Evaluating a polar double integral on the semi disc

The integral: $$\iint_D (x^2-y^2)\,dx\,dy$$ where $D$ is defined as: $$\{(x,y)\in \mathbb R^2 \mid x^2+y^2\le 1, x\ge 0\}$$ Context I have solved double integrals on quarter discs but this semi ...
1
vote
1answer
36 views

Area of a Self-intersecting Curve

I was doing some work finding the areas of rose curves. The rose curve is a polar curve given by the equation $$ r(\theta) = \cos{k\theta} $$ When $k$ is even, the area is $\pi/2$, and when $k$ is ...