# 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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### Operators in polar coordinates in n-dimensions

I want help on converting differential operators such as the reduced wave operator (L=Δ+c) and the biharmonic operator (L=Δ^2) from Cartesian to spherical coordinates in n-dimensions. For example I ...
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### Finding the area of a polar region

I am trying to find the area inside the curve $$r = 2 + \sin2\Theta + \cos3\Theta .$$ It's a very weird looking function after graphing, and I'm not quite sure how I'm supposed to proceed. There's ...
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### Parametrization of a rotating surface

What is the parametrization of a surface obtained by rotating the circle $(y − 3)^2 + z^2 = 1, x = 0$ about the z-axis. I came up with the parametrization $S(r,θ) = (r , 3+cosθ , sinθ)$, is it ...
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### How to calculate polar angle of point given a reference point?

I want to calculate polar angle of some points based on different reference points. Usually polar angle is calculated based on reference point (0,0). What is the procedure to calculate polar angle ...
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### Evaluating $\iiint_R \log\Big((x^2 + y^2 + z^2)^\frac{3}{2}\Big)\, dx\ dy\ dz$ between balls in $\Bbb R^3$

I am working on the following problem: Evaluate: $$\iiint_R \log\Big((x^2 + y^2 + z^2)^\frac{3}{2}\Big)\, dx\ dy\ dz,$$ where $R = \big\{(x, y, z) : 1 \leq x^2 + y^2 + z^2 \leq 2^2 \big\}$ is the ...
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### Polar plane spiral repitions

I'm just starting out teaching my self about the polar plane using tools like Desmos and have been wondering: When graphing an equation in the polar plane, does it extend forever? All the tools ...
Given, $\cos\theta=\frac{x}{\sqrt{x^2+y^2}}$, how can you write $\cos\frac{\theta}{n}$ (n an integer for simplicity) in terms of x and y? For example, one may say $\cos\frac{\theta}{n}=?\frac{x}{\... 1answer 70 views ### Why does the polar coordinate method not work? I tried to calculate the limit$\lim\limits_{(x,y)\rightarrow(0,0)} (x^2+y^2)^x$By using polar coordinates$ x = r \cdot \cos(\theta)y = r \cdot \sin(\theta)$resulting in$((r\cdot \cos(\...
Help me, please! how to find the distance between two points $A( x_1,y_1 )$ $B( x_2,y_2 )$ in the polar coordinate system?