# Tagged Questions

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 ($\theta$).

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### Cylinder defined on 3d coordinate plane

This is the first time, I have seen a problem like this: I feel as though if i knew where to start i would be able to do this problem easily. In other words, question 1-4 make sence to me and i ...
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### The direction of the angle in polar coordinate system? [on hold]

Polar coordinate is $(r,\theta)$.In which direction $\theta$ will be counted;clockwise or anti clockwise?
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### Diagram of a multivaribale function

I have to draw the diagram of the function: $$(x^2+y^2)^{\frac{3}{2}}=x^2-y^2$$ I transformed it with polar coordinates to: $$r=\cos^2(\varphi)-\sin^2(\varphi)$$ with $r \ge 0$ and $\cos^2 \ge sin^2$....
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### Equation of a circle in polar coordinates under a linear transformation

Let's say we translate a circle with origin $(0,0)$ on the x axis by some constant $c$. What would the new equation of the circle be in polar coordinates? I have tried subbing in the equation of the ...
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### Area of the polar figure enclosed by the circle $r=2$ and the cardioid $r=2(1+cos θ)$

This is exercise 7, of the book Engineering Mathematics by Stroud, Chapter 24, Further Problems section. Here's a graph i made of the figure as i see it: It gives the answer as $π+8$. The integral ...
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### Polar coordinates for vector field to find sticking flow

I am currently working on an impacting system which is basically just a spring damper and a circular enclosure. Because of the rotational symmetry of the problem I need the vector field in polar ...
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### Is there any way that a polar coordinate function can be shifted inward or outward without changing the derivative where it exists?

question Let f(x) be a polar coordinate function defined from 0 to pi Is there a translation that pulls f outward (like in the sense f(x) + c does) without altering the polar coordinate derivative? ...
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### Is there a way to shift a portion of a polar coordinate graph without disrupting its shape?

A polar coordinate function f(x) can be rotated around the axis by h with the shift f(x - h). However, this rotates the graph. Is there a way to shift a polar coordinate function by x and y ...
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### Calculate the area bounded by the polar curve $r(\theta)=2+\sin(\theta)$

How can I calculate the area bounded by the following curve: $$r(\theta)=2+\sin(\theta)$$
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### Converting a higher order operator to polar coordinates?

The operator: $$\frac{\partial^4}{\partial x^4}+2\frac{\partial^4}{\partial x^2 \, \partial y^2}+\frac{\partial^4}{\partial y^4}$$ ... appears in the equation of motion of an oscillating rigid ...
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### polar cordinates, finding teta

the integral,and a picture of the graph of D in the left corner you have the integral and below it the range D. the right side has the ranges i found. Hi im having a hard time understanding ...
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### Finding flux using polar coordinates.

I solved exercise using polar coordinates. I thought that $x=rcos(\alpha)$ and $y=rsin(\alpha)$. In my exercise given. Given vector field and I solved it using divergence theorem. Result is: $\iiint$...
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### Find the area of the region that is bounded by $r = \cos(\theta)$ from $0$ to $\pi/6$

Find the area of the region that is bounded by $r = \cos(\theta)$ from $0$ to $\pi/6$. I'm pretty confident that I know what I am doing for this problem but I just want to make sure I have it down. ...
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### Find the area of the region that is enclosed by:

$r = 2\cos(\theta)$ and $r = 1$ I went ahead and tried it and my answer was just $2\pi$. I was wondering if someone could check if I got it right, and if I didn't, tell me what I did wrong? ...
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### Eliminate the parameter

Given the parametric equations: $x = sin(\frac{1}{2} \theta)$ $y = cos(\frac{1}{2} \theta)$ Eliminate the parameter. I am completely lost. Please help.
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### Find polar coordinates $(r, \theta)$ of the point, where $r > 0$ and $0 \leq \theta < 2\pi$

Given these Cartesian coordinates: $(2,-3)$ This is my fourth problem of this type, I solved the other 3, but this one has weird numbers and I don't know what to do. $\tan\theta = -\frac{3}{2}$ ...
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### line integral problem, stuck in the curve

Problem: A force field is given in polar coordinates by the equation $$F(r,\theta)= (-4\sin (\theta), 4\sin (\theta)).$$ Compute the work done in moving a particle from the point $(1,0)$ to the ...
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### Is it possible to convert the polar equation $\ r = k \cos (\theta n) + 2$ into cartesian form?

Is it possible to convert the polaer equation $$\ r = k \cos (\theta n) + 2$$ into cartesian form? Here, $k$ is some constant and $n$ is any positive whole number greater than $2$. The ...
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### How do I find the Integral of $\sqrt{r^2-x^2}$?

How can I find the integral of the following function using polar coordinates ? $$f(x)=\sqrt{r^2-x^2}$$ Thanks!
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### Solve differential equation by using polar coordinates

For $\alpha, \beta>0$ the differential equation, I am trying to solve, is given by \begin{pmatrix}\dot x_1\\\dot x_2\end{pmatrix}=\alpha\sin(x_1^2+x_2^2)\begin{pmatrix}x_2\\-x_1\end{pmatrix}+\...
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### Polar Coordinates Volume of Solid, Angle for integration?

I'm trying to understand how to find the angle for the integration in polar coordinate form for a solid. Here's an example of what I'm trying to solve: Find the volume of the solid bounded by the ...
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### Cauchy rieman equation. What is u?

Using cauchy rieman equation, i want to show the function is analytic. So i want to decompose from f(z) to two term (real part and imaginary part) With rectangular form or polar form. But it is so ...
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### Cartesian and Polar Coordinates, proving the same number-pair

The question states: Prove that a necessary and sufficient condition for a point to be represented by the same number-pair (a,b) both cartesian and polar coordinates is that it lies on the initial ...
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### Solve $z^5=-32$ and draw its solutions in complex space, then describe their characteristic geometrical property.

I'm solving past exam questions in preparation for an Applied Mathematics course. I came to the following exercise, which poses some difficulty. If it's any indication of difficulty, the exercise is ...
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### Can we convert polar to rectangular when we are given $(1,\theta )$ where $r=1$ and $0\le \theta <2\pi$?

Can we convert polar to rectangular when we are given $(1,\theta )$ where $r=1$ and $0\le \theta <2\pi$?
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### How to think in terms of Polar Coordinates?

I am currently studying Polar Coordinates and many times I've noticed that one converts polar equations in cartesian form to do further analysis. Is there a way to think in terms of Polar Coordinates? ...
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### Polar angle of a given point

How to find out polar angle of a given point $A(x_1,y_1)$ relative to another point $B(x_2,y_2)$ in a 2D space?
I have been trying to convert the polar equation to rectangular. $U(1,\theta) = 10+3*sin(\theta)-10*cos(2*\theta)$ I started off my multiplying everything by r and using the trig identity for cos($... 2answers 32 views ### Intersection between roses with given polar equations$ r_1 \ = \ 4 \sin(3 \theta) \ $and$ \ r_2 \ = \ 3 \cos(3\theta) \ $a) find the solutions to the system using polar coordinates I was able to solve this by setting$ \ r_1 \ $and$ \ r_2 \ $... 2answers 30 views ### Converting polar equation to cartesian coordinates I have been trying everything to convert the polar equation$r=\frac{2}{1-\cos(\theta)}$to cartesian coordinates but I simply didn't manage to know the right answer. Please help me.. 0answers 31 views ### Evaluating an integral in polar coordinates with exponential and sec^2 I'm stuck trying to find the closed form expression of an integral. I was able to upper bound it, but if anybody can help me find a way to determine the exact answer, it would be appreciated. Thanks ... 1answer 31 views ### How to multiply a number in polar form by$-1$Given a number in the form of$a\angle b$, what happens if I multiply it by$-1$? Is it$-a\angle -b$or$a\angle −b$? Does a negative modulus even make sense? Thanks! 2answers 58 views ###$r=a\sin \thetar=a\cos \theta$intersect at right angles In Stewart's Calculus book, he asks: Show that the curves$r=a\sin \theta$,$r=a\cos \theta$at right angles. I do not understand the question. It is clear that they meet for example when$\...
Been practicing conversions from rectangular form to polar form but got stuck on one question. rectangular form: $\frac{1}{1+j\omega}$ polar form: $r = \left|\frac{1}{1+j\omega}\right|$, \$\phi = -\...