Convert unit vector from cartesian to spherical coordination

[assassin2811]

i have a problem :
A small loop antenna in free space and centered about the origin on the xy-plane is producing a
(far-field) radiation electric field (in phasor notation) :
http://postimg.org/image/63tm76h5l/

and their solution :
http://postimg.org/image/6mdm6roh9/

i don't understand how can they replace (-x^) with (∅^.sinθ), can anyone show me how to convert unit vectors in cartesian coordination (x^, y^, z^) into spherical (r^, θ^, ∅^), thanks

 

[SteamKing]

The correct terms are 'Cartesian coordinates' or 'spherical coordinates'.

See: http://en.wikipedia.org/wiki/Spherical_coordinate_system