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Section 12.13 : Spherical Coordinates

For problems 1 – 3 convert the Cartesian coordinates for the point into Spherical coordinates.

1. \(\left( {6,2, - 8} \right)\)
2. \(\left( { - 1,5,2} \right)\)
3. \(\left( { - 3, - 2,1} \right)\)
4. Convert the Cylindrical coordinates for the point \(\left( {5,1.294,6} \right)\) into Spherical coordinates.
5. Convert the following equation written in Cartesian coordinates into an equation in Spherical coordinates. \[\frac{{xz}}{y} = 2 - x\]

For problems 6 – 8 convert the equation written in Spherical coordinates into an equation in Cartesian coordinates.

1. \(\rho \cos \varphi \sin \varphi \sin \theta = 3\)
2. \(\rho - \cos \varphi = 2 + {\cos ^2}\varphi \)
3. \(\tan \varphi \left( {\cos \theta - \sin \theta } \right) = 4\)

For problems 9 & 10 identify the surface generated by the given equation.

1. \({\cos ^2}\varphi - {\sin ^2}\varphi = 0\)
2. \(\displaystyle \sin \varphi cos\theta + sin\varphi sin\theta + \cos \varphi = \frac{1}{\rho }\)