versed sine

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A geometrical illustration of the versed sine (labelled "versin")


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, Royal Society (Great Britain), Philosophical Transactions: 1750-1755, 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 ; [] .

Usage notes[edit]

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


Derived terms[edit]