Answer
$$\left( { - 2.9021,{\text{ }}2.9021,{\text{ }}11.2763} \right)$$
Work Step by Step
$$\eqalign{
& \left( {12,\frac{{3\pi }}{4},\frac{\pi }{9}} \right) \cr
& \left( {\rho ,\theta ,\phi } \right):{\text{ }}\left( {12,\frac{{3\pi }}{4},\frac{\pi }{9}} \right) \to \rho = 12,{\text{ }}\theta = \frac{{3\pi }}{4},{\text{ }}\phi = \frac{\pi }{9} \cr
& {\text{Spherical to rectangular }}\left( {\rho ,\theta ,\phi } \right) \cr
& x = \rho \sin \phi \cos \theta ,{\text{ }}y = \rho \sin \phi \sin \theta ,{\text{ }}z = \rho \cos \phi \cr
& x = \left( {12} \right)\sin \left( {\frac{\pi }{9}} \right)\cos \left( {\frac{{3\pi }}{4}} \right) \approx - 2.9021 \cr
& y = \left( {12} \right)\sin \left( {\frac{\pi }{9}} \right)\sin \left( {\frac{{3\pi }}{4}} \right) \approx 2.9021 \cr
& z = \left( {12} \right)\cos \left( {\frac{\pi }{9}} \right) \approx 11.2763 \cr
& {\text{The rectangular }}\left( {x,y,z} \right){\text{ coordinates are:}} \cr
& \left( { - 2.9021,{\text{ }}2.9021,{\text{ }}11.2763} \right) \cr} $$
