How do I calculate the distance between two points of latitude and longitude?

I've cranked through the math, and can now greatly simplify the solution.

Imagine if we spin the earth so that our first vector is at 0 degrees latitude and 0 degrees longitude. The second vector would be at (alpha2 - alpha1) degrees latitude and (beta2 - beta1) degrees latitude.

Since ...

sin(0) = 0 and cos(0) = 1

our dot product simplies to ...

cos(delta_alpha) * cos(delta_beta) = cos(theta)

The rest of the math remains unchanged.

theta = acos (cos(delta_alpha) * cos(delta_beta))
distance = radius * theta

Hope this helps.