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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