% Bernd Berg sep 12 2017.
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\centerline{\bf Special and General Relativity (PHZ 4601/5606) Fall 2017 
Solutions} \medskip

\centerline{\bf Set 3} 

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% \end{figure} \centerline{Potential as function of $z$.}

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\item{\bf 7. Spherical coordinates.}
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\item{(a)} $ x^1=-(5/4)\,\sqrt{2}\,[ly],\ 
             x^2=-(5/4)\,\sqrt{6}\,[ly],\
             x^3=-(5/2)\,\sqrt{2}\,[ly],$ \medskip

\item{(b)} $\rho = \sqrt{(x^1)^2+(x^2)^2} = \sqrt{5},\
 \theta = \tan^{-1}\left(\rho/x^3\right) = \pi - 0.6405 = 2.501,$
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$ \phi = \tan^{-1}\left(x^2/x^1\right) 
 = \tan^{-1}\left(-1/2\right) = -0.4636,\ r=\sqrt{14} .$
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