Why we kept the trig in golf: Mathematical simplicity is not always the same as conceptual simplicity

Someone read the golf example and asked: You define the threshold angle as arcsin((R – r)/x), but shouldn’t it be arctan((R – r)/x) instead? Is it just that it does not matter with these small angles, where sine and tangent are about the same, or am I missing something? My reply: This sin vs tan …