Answer to Question #151518 in Differential Geometry | Topology for Dolly

Question #151518
Find the spherical coordinates of the point whose coordinates are
1) (1, 1, √6)
2) (-2, 2√3, 4)
3) (-√3, 1, -2)
4) (4,-4√3, 6)
1
Expert's answer
2020-12-17T18:40:12-0500

We remind the expressions of spherical coordinates :

"\\rho = \\sqrt{x^2+y^2+z^2}"

"\\theta = \\arccos(\\frac{z}{\\rho})"

"\\phi" such that "x=\\rho \\sin(\\theta) \\cos(\\phi), y=\\rho\\sin(\\theta)\\sin(\\phi)"

Therefore we have :

  1. "(\\rho,\\theta,\\phi) = (2\\sqrt{2}, \\frac{\\pi}{6}, \\frac{\\pi}{4})"
  2. "(4\\sqrt{2}, \\frac{\\pi}{4}, \\frac{2\\pi}{3})"
  3. "(2\\sqrt{2}, \\frac{3\\pi}{4}, \\frac{5\\pi}{6})"
  4. "(10, \\arccos(\\frac{3}{5}), -\\frac{\\pi}{3})"

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