Solution
= Solution
Use the convention that $\theta$ is the <polar angle> from positive $z$, and $\phi$ the <azimuth> from positive $x$. The radius is
$$
r=\sqrt{\frac3{16}+\frac9{16}+\frac94}=\sqrt3.
$$
Then $\cos\theta=z/r=\sqrt3/2$, while $\tan\phi=y/x=\sqrt3$ and both planar coordinates are positive. Thus the <spherical coordinates> are
$$
\boxed{(r,\theta,\phi)=\left(\sqrt3,\frac\pi6,\frac\pi3\right)}.
$$