versed sine

From New Latin sinus versus (“flipped sine”); the sine function being sometimes called sinus rectus.

versed sine (plural versed sines)

1. (trigonometry) The trigonometric function 1 − cos(x).
   • 1753, John Robertson, “The Construction of the Logarithmic Lines on the Gunter′s Scale”, in Philosophical Transactions: 1750-1755, Great Britain: Royal Society, page 340:

     For the divisions, to be laid on this line, are the differences between the logarithm versed sine of 180°, and the logarithm versed sines of the successive arcs.

   • 1805, John William Norie, A New and Complete Epitome of Practical Navigation, page xxii:

     But if the given arch exceed 90°, find the natural co-sine of its supplement, which add to 1000000, and the sum will be the natural versed sine required.

   • 1806, John Garnett, Tables Requisite To Be Used with The Nautical Ephemeris, page 41:

     The Natural Sines in this table are fractions (radius being unit); and are particularly adapted to Dunthorne′s and other methods of clearing the moon′s distance from the effects of parallax and refraction, where natural sines or versed sines are used ; […] .

Once considered an important trigonometric function; now much less so, since the advent of calculators and computers.

• (1 − cos): vers, versin, versine

• coversed sine
• hacoversed sine
• haversed sine
• suversed

• Severnside