A look back at a long-forgotten trigonometric function: the versine function and its inverse

Extract

Ask anyone who has studied mathematics to a moderate level how many trigonometric functions there are and one is likely to be presented with a range of answers depending on what the person being asked is most likely to remember. Perhaps the ‘calculator button’ three of sine, cosine, and tangent will come to mind as these are the three trigonometric functions found on any standard scientific calculator. At a stretch, perhaps the names for their respective reciprocals, cosecant, secant and cotangent, will be recalled. Beyond the modern standard six, looking at calculus or trigonometric texts published prior to 1900 one soon discovers others going by strange names such as versine, haversine, or coversine (see, for example, [1, pp. 53, 63]). There are at least six others with as many as perhaps ten to twelve having received a name at one time or another. Today all these additional trigonometric functions considered important enough to grace the pages of texts in centuries past have fallen by the wayside, to be largely forgotten in favour of the modern standard six. Of course the pedant amongst us would say there is only one trigonometric function, the sine function, which currently stands as the preferred fundamental trigonometric entity, with all others being simple variations of this function, and they would not be incorrect in asserting this. But having the current standard six seems about the right balance between the minimalistic on the one hand and convenience on the other hand.