# Tagged Questions

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 calculate position on globe

Given position as: Latitude Longitude Height above Earth's surface; and Given direction as: Heading (i.e. azimuth angle) Pitch How can I calculate the latitude and longitude on the Earth's ...
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### Evaluate $\int _0 ^4 \int _0 ^{\sqrt {16-x^2}} \int _{\sqrt {x^2+y^2}} ^4 \sqrt {x^2+y^2+z^2} \ \Bbb d z \ \Bbb d y \ \Bbb d x$ [closed]

Evaluate $$\int \limits _0 ^4 \int \limits _0 ^{\sqrt {16-x^2}} \int \limits _{\sqrt {x^2+y^2}} ^4 \sqrt {x^2+y^2+z^2} \ \Bbb d z \ \Bbb d y \ \Bbb d x .$$ I've always had some difficulty using ...
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### Show the triple integral given is equivalent to $\frac{15\pi}{16}$

Evaluate $$\iiint_E\;z \, dV$$ where E is enclosed between the spheres $x^2 + y^2 + z^2 = 1$and$x^2 + y^2 + z^2 = 4$ in the first octant. I'll be honest. My first ...
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### Multidimensional change of variables for pdf integration

I have a very simple question, but I could not find the answer, so I have to ask this here: Given is a multidimensional pdf $f(x_1, ..., x_n)$. $x_1, ..., x_n$ are Carthesian coordinates. We want to ...
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### finding farthest vertices to a point in n-dimensional hypercube

I am an engineer not a mathematician. So, please accept my apology if this is a very simple problem for this site. Given a coordinate $A(x_{1A},x_{2A},...,x_{nA})$ and a value d in n-dimension space. ...
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### Spherical law of cosines

The spherical law of cosines states that $$\cos c = \cos a \cos b + \cos C \sin a \sin b,$$ where $a,b,c$ are sides of a spherical triangle, and $C$ the angle. Is there a proof for this theorem ...
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### Trouble with Triple integral in spherical coordinates

What is the form of triple integral to compute the volume bounded by $z=x^2+y^2$ and $z=9$ ? Also, change it to spherical coordinate?
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### Limits of integration spherical coordinates

I have seen a lot of exercises where they solve a triple integral using spherical coordinates. But I'm confused about the limits that one should use. For example when they integrate over a sphere like ...
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### Jacobian matrix for change of variables from Cartesian coordinate system to Spherical (Geographic) coordinate system.

I am trying to obtain the Jacobian matrix for a change of variables from Cartesian coordinate to spherical coordinates. My spherical coordinate system is a conventional right-handed Geographic ...
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### Equation of a great circle passing through two points

I've searched everywhere for something to help me with this problem, but I can't find anything. What I want to calculate is the midpoint between two locations (latitude and longitude) on a sphere. The ...
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### Set up the triple integral for region between cylinders $x^2 + y^2 = 9 \quad x^2 + y^2 = 16 \quad z = 4+x^2$ and $0xy$ plane

I ran into a problem that I am not sure about the correct answer. The question is: Set up the triple integral for region between $x^2 + y^2 = 9 \quad x^2 + y^2 = 16 \quad z = 4+x^2$ and $0xy$ ...
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### Volume enclosed between two spheres using spherical coordinates [duplicate]

The question reads use spherical coordinates to find the volume of the solid enclosed between the spheres $x^2+y^2+z^2=4$ and $x^2+y^2+z^2=4z$. The first sphere is a sphere of radius 2 centered at ...
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### Derivative of spherical coordinates [closed]

Why are the r dot terms (eg -r^dotsincos in the z derivative) in the derivatives of the spherical coordinates? Differentiation, as I've understood it, is differentiating a function with respect to a ...
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### Finding Surface area of a shape given its spherical coordinate equation

Is the surface area of the shape defined by $\rho = 4\cos(\theta)\sin(\theta)$ given by the following? $$\int_0^{2\pi}\int_0^\pi\sqrt{1 + 0 + 16\cos^2(2\theta)}\ \rho^2\sin(\phi)\ \ d\phi\ d\theta$$...
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### Cube in Spherical Coordinates not centred at the origin

I`ve seen that there are already a couple of questions about how to describe a cube in Spherical Coordinates. However they are all centred at the origin. I would like to describe a cube in Spherical ...
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