Here's the problem for what it is worth.
Bear with me and I'll get to the Trigonometry part.
The dipole moment is defined as
(The
is the displacement vector from the origin to the point where the charge q sits.)
Now pick a point
in three space. Specifically
The dipole term of the potential is calculated by
where
is the direction cosine of the angle between
and
. (ie. the cosine of the angle between
and the y axis, if we make the triangle form by putting the tails of
and
at the origin.)
The question then is how to write
in terms of Cartesian coordinates? I could use the Law of Cosines to find the angle if I had the length of the line between the heads of
and
. I could use the Law of Sines, but I don't have any of the angles in the triangle.
Any thoughts? Thanks!
-Dan