Paul's Online Notes
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Home / Calculus III / 3-Dimensional Space / Spherical Coordinates
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This is a little bit in advance, but I wanted to let everyone know that my servers will be undergoing some maintenance on May 17 and May 18 during 8:00 AM CST until 2:00 PM CST. Hopefully the only inconvenience will be the occasional “lost/broken” connection that should be fixed by simply reloading the page. Outside of that the maintenance should (fingers crossed) be pretty much “invisible” to everyone.

Paul
May 6, 2021

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Section 1-13 : Spherical Coordinates

For problems 1 & 2 convert the Cartesian coordinates for the point into Spherical coordinates.

  1. \(\left( {3, - 4,1} \right)\) Solution
  2. \(\left( { - 2, - 1, - 7} \right)\) Solution
  3. Convert the Cylindrical coordinates for the point \(\left( {2,0.345, - 3} \right)\) into Spherical coordinates. Solution
  4. Convert the following equation written in Cartesian coordinates into an equation in Spherical coordinates. \[{x^2} + {y^2} = 4x + z - 2\] Solution

For problems 5 & 6 convert the equation written in Spherical coordinates into an equation in Cartesian coordinates.

  1. \({\rho ^2} = 3 - \cos \varphi \) Solution
  2. \(\csc \varphi = 2\cos \theta + 4\sin \theta \) Solution

For problems 7 & 8 identify the surface generated by the given equation.

  1. \(\displaystyle \varphi = \frac{{4\pi }}{5}\) Solution
  2. \(\rho = - 2\sin \varphi \cos \theta \) Solution