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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. $$\displaystyle \sin \varphi cos\theta + sin\varphi sin\theta + \cos \varphi = \frac{1}{\rho }$$