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### Section 12.13 : Spherical Coordinates

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

1. $$\left( {3, - 4,1} \right)$$ Solution
2. $$\left( { - 2, - 1, - 7} \right)$$ Solution
3. Convert the Cylindrical coordinates for the point $$\left( {2,0.345, - 3} \right)$$ into Spherical coordinates. Solution
4. Convert the following equation written in Cartesian coordinates into an equation in Spherical coordinates. ${x^2} + {y^2} = 4x + z - 2$ Solution

For problems 5 & 6 convert the equation written in Spherical coordinates into an equation in Cartesian coordinates.

1. $${\rho ^2} = 3 - \cos \varphi$$ Solution
2. $$\csc \varphi = 2\cos \theta + 4\sin \theta$$ Solution

For problems 7 & 8 identify the surface generated by the given equation.

1. $$\displaystyle \varphi = \frac{{4\pi }}{5}$$ Solution
2. $$\rho = - 2\sin \varphi \cos \theta$$ Solution