Chris Veness' discussion of using the spherical law of cosines (http://www.movable-type.co.uk/scripts/latlong.html) suggests it gives well-conditioned results "around 1 metre" in JavaScript (this assumes a sphere with 6,371km radius).
In Chrome 33, Math.pow(Math.cos(Math.PI / 4), 2) yields 0.4999999999999999. When we take the arccosine of twice this, we get something significantly different than zero. Multiplying by 6371 means we can't assert that this is within 1e-9 of zero.
