Mathematics: Find an equation in spherical coordinates for the equation given in rectangular coordinates. x^2+y2+z^2-3z=0

The *standard error* must also increase if the standard deviation of a population increases....

Find an equation in spherical coordinates for the

QueenNerdy889

12.03.2022

We have been given the equation in rectangular coordinates as

x^2+y^2+z^2-3z=0

In Spherical coordinates, we know that

$x=\rho \sin \phi \cos \theta\\
y=\rho \sin \phi \sin \theta\\
z=\rho \cos \phi\\
x^2+y^2+z^2=\rho^2$

On substituting these values in the given equation, we get

(x^2+y^2+z^2)-3z=0

$\rho^2- 3\rho \cos \phi=0\\
\\
\rho^2= 3\rho \cos \phi\\
\\
\rho = 3 \cos \phi$

Thus, the equation in spherical coordinates is given by

$\rho = 3 \cos \phi$

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