As you may have guessed, there is a simple formula for expressing great-circle distance directly in terms of longitude and latitude. Let (α1, β1) and (α2, β2) be the longitude-latitude coordinates of two points on the surface of the earth, where we interpret N an E as positive an S and W as negative. Show that the great-circle distance between these points is 3960γ miles, where 0 ≤ γ ≤ π and
cos γ = cos(α1 - α2) cos β1 cos β2 + sin β1 sin β2