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coversed sine



A plot of the versed sine (versin) and coversed sine (coversin) between -3π and 3π


From contraction of complement + versed sine.


coversed sine (plural coversed sines)

  1. (trigonometry) The trigonometric function 1 − sin(x).
    • 1825, Jas Thomson, Elements of Plane and Spherical Trigonometry[1], page 2:
      The cosine of an arc is the sine of its complement.† In like manner, the coversed sine, cotangent, and cosecant of an arc, are respectively the versed sine, tangent, and secant of its complement.
    • 1830, W. Hopkins, Book II: Elements of Trigonometry, of Geometry, Plane, Solid, and Spherical, page 46,
      At the top of the page on the left-hand side is placed the number of degrees, and in the left-hand column each minute of the degree, opposite to which are arranged the numerical values of the sine, coversed sine, &c, of the corresponding angle in those columns, at the top of which those terms are placed.
    • 1838, William Grier, The Mechanic′s Pocket Dictionary[2], page 21:
      For the coversed sine; subtract the sine of the angle from 1. Thus, for the same angle we have the coversed sine,
      1 — ·36650 = ·6335.
    • 1871, Homersham Cox, The Law and Science of Ancient Lights, 2nd Edition, page 109,
      Hence the cosines and versed sines of zenith distances are respectively equal to the sines and coversed sines of the corresponding angular elevations.


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