Question

Identify the surface whose equation is given. \rho= \sin \theta \sin \phi

First order differential equations
ANSWERED
asked 2021-05-31
Identify the surface whose equation is given.
\(\rho= \sin \theta \sin \phi\)

Answers (2)

2021-06-01
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Best answer
2021-09-09

Multiply both sides by p and you'll get \(p^2=p\sin(\phi)\sin(\theta)\), which translates to \(x^2+y^2+z^2=y\), remember \(p\sin(\phi)\sin(\theta)=y\) in cartesian coordinates,

So now we have a sphere here, to find its center and radius you have to complete the square.

\(x^2+y^2-y+z^2=0\) which gives \(x^2+y^2-y+\frac{1}{4}+2^2=\frac{1}{4}\) now we have to factor and we get \(x^2+(y-\frac{1}{2})^2+2^2=\frac{1}{4}\)

This is a sphere centered at \((0,\frac{1}{2},0)\) with radius \(\frac{1}{2}\)

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