One of the three formulas I remember learning in the dark ages:

*x = rho cos(phi) sin(theta)*

*y = rho sin(phi) sin(theta)*

*z = rho cos (theta)*

We know this from geometry but we could also square everything and sum it to get:

*rho = sqrt(x^2 + y^2 + z^2)*

This lets us solve for theta pretty easily:

*cos(theta) = z / sqrt(x^2 + y^2 + z^2)*

Because sin^2 + cos^2 = 1 we can get:

*sin(theta) = sqrt(1 - z^2/( x^2 + y^2 + z^2))*

phi we can also get from geometry using the ever useful atan2:

*phi = atan2(y, x)*

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