ARTIKELDIGITAL.COM

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...

engineer Charles Haslett, who used it in conjunction with the existing versine function, vers ⁡ θ = 1 − cos ⁡ θ {\displaystyle \operatorname {vers} \theta...

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...

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...

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...

(6th century AD), who discovered the sine function, cosine function, and versine function. During the Middle Ages, the study of trigonometry continued in...

(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)...

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...

tangent, cotangent, secant, and cosecant, as well as archaic functions like versine and exsecant – can be defined geometrically in terms of a unit circle,...

Quadrant from 1840s Ottoman Turkey with axes for looking up the sine and versine of angles...

(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...

}{2}}\right)\,\sin \left({\frac {\gamma }{2}}\right)\end{aligned}}} The versine, coversine, haversine, and exsecant were used in navigation. For example...

rotating in a convex closed curve Circle graph Exsecant and excosecant Versine and haversine – ( crd ⁡ θ = 2 haversin ⁡ θ {\displaystyle \operatorname...

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...

Ver (command), a shell command in DOS, Windows etc. an abbreviation for "versine", a trigonometric function ver (function prefix) (versus), a prefix for...

needed] Trigonometric functions: The trigonometric functions sine and versine originated in Indian astronomy. Codex Sinaiticus and the Codex Vaticanus...

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...

or use alternate methods. Arcsine distribution Inverse exsecant Inverse versine Inverse hyperbolic functions List of integrals of inverse trigonometric...

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...

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...

also known as the cofunction identities. This also holds true for the versine (versed sine, ver) and coversine (coversed sine, cvs), the vercosine (versed...

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...

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)...

Regiomontanus used nearly the modern form, but written in terms of the versine, ⁠ vers ⁡ x = 1 − cos ⁡ x {\displaystyle \operatorname {vers} x=1-\cos...

calculations for certain input values see trigonometric functions like versine and exsecant. Weisstein, Eric W. "Natural Logarithm". mathworld.wolfram...

tributary of the Lot Vers, an abbreviation for the trigonometric function versine Vers, an abbreviation for versatile, commonly used in Western gay male...

sine, cosine, tangent, cotangent, secant, cosecant, exsecant, excosecant, versine, coversine, vercosine, covercosine, haversine, hacoversine, havercosine...

measures of angles, made their calculations differently, "introduced the versine, which is the difference between the radius and cosine, and discovered...

as vercos.) ver – versine function. (Also written as vers, siv.) vercos – vercosine function. (Also written as vcs.) vers – versine function. (Also written...

table. The result is accurate to the four digits given. Skinny triangle Versine Exsecant Holbrow, Charles H.; et al. (2010), Modern Introductory Physics...

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...

quadric surface specified by R {\displaystyle R} and K {\displaystyle K} . Versine Chord Barbastathis, George; Sheppard, Colin. "Real and Virtual Images"...

of the complement", suggesting the similarity to kojyā is coincidental. Versine B.B. Datta and A.N. Singh (1983). "Hindu Trigonometry" (PDF). Indian Journal...

complexity. Trigonometric functions – The trigonometric functions sine and versine originated in Indian astronomy along with the cosine and inversine , adapted...

{\displaystyle (1-\cos \theta )} can be calculated without cancellation as the versine function: versin ⁡ θ = 1 − cos ⁡ θ = 2 sin 2 ⁡ θ 2 {\displaystyle \operatorname...

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...

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...

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...

function Inverse trigonometric functions Jyā, koti-jyā and utkrama-jyā Versine Trigonometric identity (list) De Moivre's formula Euler's formula Hermite's...

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...

\operatorname {exsec} (x)} sec ⁡ ( x ) − 1 {\displaystyle \sec(x)-1} - Versine vers ⁡ ( x ) {\displaystyle \operatorname {vers} (x)} 1 − cos ⁡ ( x ) {\displaystyle...

_{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...

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...

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)...

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...

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...

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...

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...

}{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...

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...