Here's the problem for what it is worth.
Bear with me and I'll get to the Trigonometry part.Diagram: Let there be a point charge of -q at the coordinates (x,y) = (a, 0), a point charge of -q at (-a, 0), and a point charge of 2q at (0, L). Find the dipole moment ( ) term of the electric potential and put it in terms of Cartesian coordinates.
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!