spherical law of cosines is the formula used to calculate the distance between two points on the earth. I've been looking for a reference that discuss about the coordinate system is used in that formula, but no one has discussed what the coordinates systems used by the formula. can anyone help me please???
What coordinate system is used in the spherical law of cosines?
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http://en.wikipedia.org/wiki/Spherical_trigonometry
Under Cosine rules & sine rules look under Derivation of the cosine
They use the cartesian coordinate system for their proof. They target the distance between points B & C defined by the dot product of dot(b, c) = |b|*|c|*cos a, but given that they're unit vectors with both vectors b & vector c being of length 1, that equates to dot(b, c) = 1 * 1 * cos a => dot(b, c) = cos a. Positions of vector B & vector C are determined using the cartesian coordinate system to determine that angle a representing the distance, just follow the proof.