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Search references for VERSINE. Phrases containing VERSINE
See searches and references containing VERSINE!VERSINE
1 minus the cosine of an angle
Look up versine or versed sine in Wiktionary, the free dictionary. The versine or versed sine is a trigonometric function found in some of the earliest
Versine
Trigonometric function defined as secant minus one
engineer Charles Haslett, who used it in conjunction with the existing versine function, vers θ = 1 − cos θ , {\displaystyle \operatorname {vers}
Exsecant
Formula for the great-circle distance between two points on a sphere
be written in terms of any multiple of the haversine, such as the older versine function (twice the haversine). Prior to the advent of computers, the elimination
Haversine_formula
(sixth century AD), who discovered the sine function, cosine function, and versine function.[citation needed] During the Middle Ages, the study of trigonometry
History_of_trigonometry
Distance from an arc's midpoint to the midpoint of its chord
may also be calculated from the versine function, for an arc that spans an angle of Δ = 2θ, and coincides with the versine for unit circles. Generally, for
Sagitta_(geometry)
Geometric line segment whose endpoints lie on a circular arc
rotating in a convex closed curve Circle graph Exsecant and excosecant Versine and haversine – ( crd θ = 2 haversin θ {\displaystyle \operatorname
Chord_(geometry)
Country in South Asia
using a pre-Ptolemaic Greek table of chords, produced tables of sines and versines, from which it was trivial to derive cosines. This new system of trigonometry
India
Indian mathematician-astronomer (476–550)
(kojya), versine (utkrama-jya), and inverse sine (otkram jya) influenced the birth of trigonometry. He was also the first to specify sine and versine (1 − cos x)
Aryabhata
Circle with radius of one
tangent, cotangent, secant, and cosecant, as well as archaic functions like versine and exsecant – can be defined geometrically in terms of a unit circle,
Unit_circle
Functions of an angle
(180–125 BCE) and Ptolemy of Roman Egypt (90–165 CE). The functions of sine and versine (1 − cosine) are closely related to the jyā and koti-jyā functions used
Trigonometric_functions
}{2}}\right)\,\sin \left({\frac {\gamma }{2}}\right)\end{aligned}}} The versine, coversine, haversine, and exsecant were used in navigation. For example
List of trigonometric identities
List_of_trigonometric_identities
Topics referred to by the same term
Ver (command), a shell command in DOS, Windows etc. an abbreviation for "versine", a trigonometric function ver (function prefix) (versus), a prefix for
Ver
Fundamental trigonometric functions
Quadrant from 1840s Ottoman Turkey with axes for looking up the sine and versine of angles
Sine_and_cosine
of track which typically feature a mix of small positive and negative versines. A standard chord length is used: in the UK this is conventionally 30 metres
Hallade_method
Topics referred to by the same term
COS cell lines cos x−1 = cos(x)−1 = −(1−cos(x)) = −ver(x) or negative versine of x, the additive inverse (or negation) of an old trigonometric function
Cos-1
Inverse functions of sin, cos, tan, etc.
or use alternate methods. Arcsine distribution Inverse exsecant Inverse versine Inverse hyperbolic functions List of integrals of inverse trigonometric
Inverse trigonometric functions
Inverse_trigonometric_functions
French mathematician (1667–1754)
inter x & t determinatur." (Let x be the versine of any arc [i.e., x = 1 – cos θ ]. [Let] t be the versine of another arc. [Let] 1 be the radius of the
Abraham_de_Moivre
Trigonometric function paired with another
also known as the cofunction identities. This also holds true for the versine (versed sine, ver) and coversine (coversed sine, cvs), the vercosine (versed
Cofunction
14th–16th-century Asian cultural movement
armillary and solsticial armillary of Mo'ayyeduddin Urdi, the sine and versine instrument of Urdi, the sextant of al-Khujandi, the Fakhri sextant at the
Timurid_Renaissance
Simplification of the basic trigonometric functions
table. The result is accurate to the four digits given. Skinny triangle Versine Exsecant Holbrow, Charles H.; et al. (2010), Modern Introductory Physics
Small-angle_approximation
Simple curve of Euclidean geometry
angle (since the central angle is 180°). The sagitta (also known as the versine) is a line segment drawn perpendicular to a chord, between the midpoint
Circle
One hundred years, from 301 to 400
needed] Trigonometric functions: The trigonometric functions sine and versine originated in Indian astronomy. Codex Sinaiticus and the Codex Vaticanus
4th_century
Cubic plane curve
the sail, but Grandi may have instead intended merely to refer to the versine function that appeared in his construction. In 1748, Maria Gaetana Agnesi
Witch_of_Agnesi
Area of geometry, about angles and lengths
seldom used today. These include the chord (crd θ = 2 sin θ/2), the versine (vers θ = 1 − cos θ = 2 sin2 θ/2) (which appeared in the earliest tables)
Trigonometry
sine, cosine, tangent, cotangent, secant, cosecant, exsecant, excosecant, versine, coversine, vercosine, covercosine, haversine, hacoversine, havercosine
List of mathematical functions
List_of_mathematical_functions
Logarithm to the base of the mathematical constant e
calculations for certain input values see trigonometric functions like versine and exsecant. Weisstein, Eric W. "Natural Logarithm". mathworld.wolfram
Natural_logarithm
Topics referred to by the same term
tributary of the Lot Vers, an abbreviation for the trigonometric function versine Vers, an abbreviation for versatile, commonly used in Western gay male
Vers
Mathematical relation in spherical triangles
Regiomontanus used nearly the modern form, but written in terms of the versine, vers x = 1 − cos x {\displaystyle \operatorname {vers} x=1-\cos
Spherical_law_of_cosines
Sanskrit text on Indian astronomy
measures of angles, made their calculations differently, "introduced the versine, which is the difference between the radius and cosine, and discovered
Surya_Siddhanta
as vercos.) ver – versine function. (Also written as vers, siv.) vercos – vercosine function. (Also written as vcs.) vers – versine function. (Also written
List of mathematical abbreviations
List_of_mathematical_abbreviations
quadric surface specified by R {\displaystyle R} and K {\displaystyle K} . Versine Chord Barbastathis, George; Sheppard, Colin. "Real and Virtual Images"
Sagitta_(optics)
Topics referred to by the same term
Dutch-designed glider that first flew in 1960 USNS Sagitta (T-AK-87) (1944–1959) Versine, a trigonometric function Sagitta, pseudonym of Scottish-German author
Sagitta_(disambiguation)
Development of mathematics in South Asia
half an angle and half a chord. Defined the cosine (kojya). Defined the versine (utkrama-jya). Defined the inverse sine (otkram jya). Gave methods of calculating
Indian_mathematics
Lists of values of mathematical functions
some early trigonometric tables used not sine and cosine, but sine and versine. A quick, but inaccurate, algorithm for calculating a table of N approximations
Trigonometric_table
Trigonometric functions introduced by Indian mathematicians and astronomers
of the complement", suggesting the similarity to kojyā is coincidental. Versine B.B. Datta and A.N. Singh (1983). "Hindu Trigonometry" (PDF). Indian Journal
Jyā,_koti-jyā_and_utkrama-jyā
he claimed would run forever. The trigonometric functions of sine and versine, from which it was trivial to derive the cosine, were used by the mathematician
History of science and technology on the Indian subcontinent
History_of_science_and_technology_on_the_Indian_subcontinent
Indian inventions
complexity. Trigonometric functions – The trigonometric functions sine and versine originated in Indian astronomy along with the cosine and inversine , adapted
List of Indian inventions and discoveries
List_of_Indian_inventions_and_discoveries
Vertical distance between top of the platform and top of the rail
high. Both specifications apply to straight sections with allowances for versine, end throw and cant on curves. Platforms for long-distance trains are 200 mm
Railway_platform_height
Mathematics used in Ancient China
arc of a circle s by s = c + 2v2/d, where d is the diameter, v is the versine, c is the length of the chord c subtending the arc. Sal Restivo writes
Chinese_mathematics
Overview of and topical guide to trigonometry
function Inverse trigonometric functions Jyā, koti-jyā and utkrama-jyā Versine Trigonometric identity (list) De Moivre's formula Euler's formula Hermite's
Outline_of_trigonometry
Textbook by Augustin-Louis Cauchy (1821)
cosine with the coversed sine. Cauchy originally defined the sinus versus (versine) as siv(θ) = 1 − cos(θ) and the cosinus versus (what is now also known
Cours_d'analyse
_{k=1}^{\infty }{\frac {(-1)^{k-1}z^{2k}}{(2k)!}}=\operatorname {ver} z} (versine) ∑ k = 1 ∞ ( − 1 ) k − 1 z 2 k 2 ( 2 k ) ! = hav z {\displaystyle \sum
List_of_mathematical_series
\operatorname {exsec} (x)} sec ( x ) − 1 {\displaystyle \sec(x)-1} - Versine vers ( x ) {\displaystyle \operatorname {vers} (x)} 1 − cos ( x ) {\displaystyle
List_of_periodic_functions
Persian astronomer and mathematician (c. 1380–1429)
armillary and solsticial armillary of Mo'ayyeduddin Urdi, the sine and versine instrument of Urdi, the sextant of al-Khujandi, the Fakhri sextant at the
Jamshid_al-Kashi
2nd century AD trigonometric table
late 1500s Greek mathematics Madhava's sine table Ptolemy Scale of chords Versine Toomer, G. J. (1998), Ptolemy's Almagest, Princeton University Press, ISBN 0-691-00260-6
Ptolemy's_table_of_chords
Han Chinese subdivision
arc of a circle s by s = c + 2v2/d, where d is the diameter, v is the versine, c is the length of the chord c subtending the arc. Xu Guangqi (1562–1633)
Wu_Chinese-speaking_people
kalpa Jīvā-janma: derivation of 36 sines Jīvā-vidhā: values of sines and versine Graha-sphuṭī-karma: changes in the size of epicycles according to the quadrant
Garga-samhita (Garga and Bharadvaja)
Garga-samhita_(Garga_and_Bharadvaja)
Geometry of road design
}{2}}\right)}}-1\right)} The quantity 1 − cos θ {\displaystyle 1-\cos \theta } is the versine and 1 / cos θ − 1 {\displaystyle 1/\!\cos \theta -1} is the exsecant
Geometric_design_of_roads
French noble governor and commander (1500-1563)
1563. Madeleine de Suze was the daughter of Philippe de Suze, sieur de La Versine and Claude de Villiers. He had issue: François de Monchy (–1552), murdered
Jean_de_Monchy
VERSINE
VERSINE
VERSINE
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Boy/Male
Tamil
Lord Shiva
Girl/Female
Indian
Guardian, Protector
Boy/Male
Hindu, Indian
Type of Liquid
Boy/Male
Muslim
Scholar
Girl/Female
American, Australian, British, Celtic, Danish, English, Finnish, German, Hebrew, Irish, Latin, Swedish
Of the Sea; Sea of Bitterness; From the God Mars; Bitter; Variant of Maria; Wished for Child
Girl/Female
Anglo Saxon American Celtic Latin Welsh French English Arthurian Legend
Bird.
Surname or Lastname
German and Dutch
German and Dutch : from Middle High German bloch, Middle Dutch blok ‘block of wood’, ‘stocks’. The surname probably originated as a nickname for a large, lumpish man, or perhaps as a nickname for a persistent lawbreaker who found himself often in the stocks.English : possibly a metonymic occupational name for someone who blocks, as in shoemaking and bookbinding, from Middle English blok ‘block’.Jewish (Ashkenazic) : Americanized spelling of Bloch (see Vlach).Adriaen Coertsz Block was a Dutch-born merchant-explorer who traded along the CT coast and Long Island shortly after Hudson’s voyage to the region in 1609. Block Island, between the north fork of Long Island and RI, which he used as a base of operations, is named after him.
Girl/Female
Irish
Light.
Surname or Lastname
English
English : variant spelling of Layland.
Boy/Male
Hindu, Indian, Marathi
Greatness; Majesty
VERSINE
VERSINE
VERSINE
VERSINE
VERSINE