Problem:
Convert the following vector to spherical coordinates $(x, y, z) = (\frac{1}{\sqrt{2}}, \frac{1}{4}, \frac{1}{4})$
Answer:
$\left\{\frac{\sqrt{\frac{5}{2}}}{2},\tan ^{-1}(3),\tan ^{-1}\left(\frac{1}{2 \sqrt{2}}\right)\right\}$
{'source': 'AMPS', 'file': 'amps/mathematica/algebra/spherical_coordinates/9427.txt'}