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Section 12.12 : Cylindrical Coordinates

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

1. \(\left( { - 3,5, - 8} \right)\)
2. \(\left( {4,1,7} \right)\)
3. Convert the following equation written in Cartesian coordinates into an equation in Cylindrical coordinates. \(\displaystyle \frac{{x - y}}{{{x^2} + {y^2} + 1}} = xyz\)

For problems 4 – 6 convert the equation written in Cylindrical coordinates into an equation in Cartesian coordinates.

1. \(z{r^3}\cos \left( \theta \right) = 4r + 8\)
2. \({r^2} - 3\sin \left( \theta \right) = {z^3} + \sqrt {{r^2} + 1} \)
3. \(\tan \left( \theta \right) + 2z = 1 - {r^2}\)

For problems 7 – 9 identify the surface generated by the given equation.

1. \(z = - 4r,\,\,\,z < 0\)
2. \(\displaystyle 2r + 6\cos \left( \theta \right) + 18\sin \left( \theta \right) = \frac{{51}}{r}\)
3. \(\theta = \frac{\pi }{3}\)