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Section 12.12 : Cylindrical Coordinates

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

  1. \(\left( {4, - 5,2} \right)\) Solution
  2. \(\left( { - 4, - 1,8} \right)\) Solution
  3. Convert the following equation written in Cartesian coordinates into an equation in Cylindrical coordinates. \[{x^3} + 2{x^2} - 6z = 4 - 2{y^2}\] Solution

For problems 4 & 5 convert the equation written in Cylindrical coordinates into an equation in Cartesian coordinates.

  1. \(z\,r = 2 - {r^2}\) Solution
  2. \(\displaystyle 4\sin \left( \theta \right) - 2\cos \left( \theta \right) = \frac{r}{z}\) Solution

For problems 6 & 7 identify the surface generated by the given equation.

  1. \({r^2} - 4r\cos \left( \theta \right) = 14\) Solution
  2. \(z = 7 - 4{r^2}\) Solution