Answer
$$\left( {3, - \frac{\pi }{4},\frac{\pi }{2}} \right)$$
Work Step by Step
$$\eqalign{
& \left( {3, - \frac{\pi }{4},0} \right) \cr
& \left( {r,\theta ,z} \right):{\text{ }}\left( {3, - \frac{\pi }{4},0} \right) \to r = 3,{\text{ }}\theta = - \frac{\pi }{4},{\text{ }}z = 0 \cr
& {\text{Cylindrical to spherical }}\left( {\rho ,\theta ,\phi } \right),{\text{ }}\left( {r \geqslant 0} \right){\text{ See page 807}} \cr
& \rho = \sqrt {{r^2} + {z^2}} ,{\text{ }}\theta = \theta ,{\text{ }}\phi = \arccos \left( {\frac{z}{{\sqrt {{r^2} + {z^2}} }}} \right) \cr
& \rho = \sqrt {{{\left( { - 3} \right)}^2} + {{\left( 0 \right)}^2}} = 3 \cr
& \theta = - \frac{\pi }{4} \cr
& \phi = \arccos \left( {\frac{0}{3}} \right) = \frac{\pi }{2} \cr
& {\text{The spherical }}\left( {\rho ,\theta ,\phi } \right){\text{ coordinates are:}} \cr
& \left( {3, - \frac{\pi }{4},\frac{\pi }{2}} \right) \cr} $$
