Let us consider the spherical polar co-ordinate of the point are \( (r,\ \theta,\ \phi) \).

Now given that the Cartesian co-ordinate of that point are,

\( x=1,\ y=0,\ z=\sqrt{3} \)

We know that,

\( r=\sqrt{x^2+y^2+z^2}=\sqrt{1^2+0^2+{\sqrt{3}}^2}=\sqrt{4}=2 \)

\( \displaystyle{\tan\theta=\frac{\sqrt{x^2+y^2}}{z}=\frac{1^2+0^2}{\sqrt{3}}=\frac{1}{\sqrt{3}}} \)

\( or,\ \tan\theta=\tan{30^{\circ}} \)

\( or,\ \theta=30^{\circ} \)

and,

\( \displaystyle{\tan{\phi}=\frac{y}{x}=0} \)

\( or,\ \tan\phi=\tan{0^{\circ}} \)

\( or,\ \phi=0^{\circ} \)

So the spherical polar co-ordinates of the given point are \( (2,\ 30^{\circ},\ 0^{\circ}) \)

[ To know the relation between cartesian co-ordinates and the spherical polar co-ordinates (CLICK HERE) ]