# Questions tagged [spherical-coordinates]

Questions on spherical coordinates, a three-dimensional coordinate system where a point is represented in terms of its distance from the origin, and its latitude and longitude angles (or complements thereof).

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### How to express unit vectors as partial derivatives in spherical coordinates?

In some General Relativity text, I found that the unit vectors are expressed as partial derivatives. In particular, an axisymmetric problem was dealt with using spherical coordinates, where the unit ...
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### Integral on the sphere of $\cos^n(\theta)$

I'm struggling with an integral. I have reduced it to the form $$\int \cos^n(\theta)d\Omega d\rho$$ over the unit sphere, where $\theta$ is the angle associated to the $z$-axis. The radial integral ...
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### Convex hull and bounding circle of a set of points on a sphere?

Given a finite set of random points on the unit sphere (defined in spherical coordinates), are there formulas giving the center and radius of the smallest circle (on the sphere) that contains all of ...
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### How can I calculate my position, if I have 3 points coordinates and distance? [closed]

How can I calculate my position, if I have 3 points coordinates and distance from every coordinate to my position. All coordinates by longitude and latitude.This is example
1 vote
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### Equation to convert longitude and latitude of any point if The Great Pyramid is the new north pole [closed]

In GCS coordinate system the North Pole is +90, +0; Great Pyramid of Giza is +29.9, +31.1; and ...
1 vote
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### Range of $\phi, \theta$ in $\int_0^{\pi/4} \int_0^{\pi/2} \int_0^{2\sin\phi \sin\theta} \rho^3\sin\phi \sin\theta d\rho d\theta d\phi$

The question: A solid bounded by the (y,z)-plane, the (x,y)-plane, the cone $x^2 + y^2 = z^2$, and the surface $x^2 + y^2 + z^2 - 2y = 0$. Suppose a density of a chunk of metal of the shape of this ...
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1 vote
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### If $(r,\theta,\phi)$ are spherical coordinates representing $(c_1, c_2, c_3)$, what is the difference between $(c_1, c_2, c_3)$ or $(r,\theta,\phi)$?

In the Cartesian coordinate system we identify a point in space by the three coordinates $x$, $y$, and $z$. In the spherical coordinate system, we identify a point in space by the three coordinates $r$...
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### Find angle between vectors

Let $v_1\cdots v_6$ be six unit vectors in $3$D and $\theta_{ij}$ denote the angle between the vectors $v_i$ and $v_j$. These vectors will form, in total, $^6C_2=15$ angles between them. Suppose we ...
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### How to calculate the middlle coordinate/point on earth between two coordinates? [closed]

Good Afternoon. I need help for a component of my math IA. I need to calculate the middle point between two coordinates on earth to make calculations based on this. I (stupidly) attempted to use the ...
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### How do I change a 3D equation into a Spherical coordinates

I know how to change 2D Cartesian equations into polar equations, however I'm having some difficulty with a 3D equation and converting that into a Spherical coordinate system. I am trying to take the ...
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### Flux of a vector field over a sphere

I have been given $\bar{F}=x\hat{x}+xy\hat{y}+xyz\hat{z}$, and I need to compute the flux over a sphere of radius $2$ which I assume is centered at the origin. I have already computed this using the ...
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1 vote
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### Triple integral $\iiint 2x$ $dxdydz$ on the region of space defined by $S={x^2 +y^2 + z^2 \le 1 }$
I have done the following triple integral $\displaystyle \iiint 2x ~dx~dy~dz~$ on the region defined by $S={x^2 +y^2 + z^2 \le 1 }$. Turning to the spherical coordinates I get  \left\{ \begin{...