# Questions tagged [polar-coordinates]

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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### Spiral enlargements on desmos

If you toggle the slider for n the point moves in a spiral. Is there a way to plot the curve for all values of n? https://www.desmos.com/calculator/kmdmfazsyy
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### Rotating polar velocity vector fields

There is a great way to rotate a Cartesian vector field about the origin described in Rotating vector functions. Instead, let us suppose that we have a velocity vector field in polar coordinates i.e., ...
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### How does the ellipsis $x^2+2y^2=2$ gets represented to $x=\sqrt{2}\cos\theta; y= \sin(\theta)$ in polar coordinates?

Just like the title says, How does the ellipsis with equation $$x^2+2y^2=2$$ becomes represented as $$x=\sqrt{2}\cos\theta; y= \sin(\theta)$$ in polar coordinates? can someone help me to understand ...
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### Express Laplacian in polar coordinates

Part of this problem is asking to express $u$ in polar coordinates and express the domain and BCs to those coordinates. The PDE is the Laplacian on disc with BC $u=0$: $\Delta u+\lambda u=0, \quad$ ...
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### Length of a line to the surface of a sphere when line does not originate from center

Finding Length of a line to the surface of a sphere when line does not originate from center. Here is what I know: I have a 3D sphere of radius $7$ I have a line (...
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### Why does Spivak claim there's a definable tangent line through $(0,0)$ for the graph of the polar coordinates described by $f(\theta)=|\cos(2\theta)|$

There is a problem in the Chapter 12 Appendix of Spivak's 4th Ed. Calculus (Problem 6b) that asks the reader to consider the tangent lines of different graphs of polar coordinates. For the polar ...
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### Double and triple integral in spherical polar coordinates, $\iint\sqrt{4-x^2-y^2}\mathrm{d}A$

Consider the double integral $$I=\iint\limits_{\mathcal D} \sqrt{4-x^2-y^2}\mathrm{d}A$$ where $\mathcal D=\{(x,Y): x^2 + y^2 \leq 4\}$ is the disc on the $xy$ plane (source) A.) Use polar ...
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### Show that $\int_0^{\pi/6} \frac{\tan(t)}{\sqrt{\cos(2t)}}dt = \frac{\sin^{-1}1/3}{2}$

I am aware of half-angle identities as well as the identity $\cos (2t)=\cos^{2}t-\sin^{2}t$ but I'm quite lost on how to proceed.
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### How do we describe the region of integration of the proposed triple integral? [closed]

When finding the volume outside the cylinder $x^2+y^2=25$ and inside the sphere $x^2+y^2+z^2=100$, the bounds are: $0 \leq \theta \leq 2\pi$ and $5 \leq r \leq 10$ What are the bounds for $z$?
I am trying to follow an example that does not show how a set of dynamics equations is converted to polar coordinates: $\theta=\tan^{-1}\frac{x_2}{x_1}$ \$\frac{d}{dt}\tan\theta=(\frac{1}{\cos\theta})^{...