Razlika između verzija stranice "Versinus i haversinus"

* '''Obrnuti kosinus''',<ref name="Weisstein_vercos" /> ili '''vercosinus''',<ref name="Weisstein_vercos" /><ref group="nb" name="vercosine vs. coversine" /> koji se zapisuje kao '''vercosin(''&#x3B8;'')''', '''vercos(''&#x3B8;'')'''<ref name="Weisstein_vercos">{{cite web|url=http://mathworld.wolfram.com/Vercosine.html|title=Vercosine|publisher=[[Wolfram Research, Inc.]]|dead-url=no|author-first=Eric W.|author-last=Weisstein|author-link=Eric W. Weisstein|work=[[MathWorld]]|access-date=2015-11-06|archive-url=https://web.archive.org/web/20140324181952/http://mathworld.wolfram.com/Vercosine.html|archive-date=2014-03-24}}</ref> ili '''vcs(''&#x3B8;'')'''<ref name="Shaneyfelt" />

* '''Koverzirani sinus''',<ref group="nb" name="vercosine vs. coversine" /> '''coversinus''',<ref name="Abramowitz_1972" /><ref name="Tapson_2004" /><ref name="Atlas_2009" /><ref name="Clagett_1969" /><ref name="Precalc_1999" /><ref name="Weisstein_covers" /> '''naspramni kosinus'''<ref name="Cauchy_1821" /><ref name="Bradley_2009" /><ref group="nb" name="vercosine vs. coversine" />, koji se zapisuje kao '''coversin(''&#x3B8;'')''',<ref name="Weisstein_hacoversin" />'''covers(''&#x3B8;'')''',<ref name="Abramowitz_1972" /><ref name="Tapson_2004">{{cite web|url=http://www.cleavebooks.co.uk/dictunit/notesa.htm#others|title=Background Notes on Measures: Angles|date=2004|publisher=Cleave Books|dead-url=no|author-first=Frank|author-last=Tapson|version=1.4|access-date=2015-11-12|archive-url=https://web.archive.org/web/20070209051219/http://www.cleavebooks.co.uk/dictunit/notesa.htm|archive-date=2007-02-09}}</ref><ref name="Atlas_2009" /><ref name="Korn_2000" /><ref name="Cajori_1929">{{anchor|Cajori-1929}}{{cite book|url=https://books.google.com/books?id=bT5suOONXlgC|title=A History of Mathematical Notations|date=1952|publisher=[[Open court publishing company]]|isbn=978-1-60206-714-1|edition=2 (3rd corrected printing of 1929 issue)|volume=2|location=Chicago, USA|page=172|id=1602067147|quote=The haversine first appears in the tables of logarithmic versines of [[José de Mendoza y Rios]] (Madrid, 1801, also 1805, 1809), and later in a treatise on navigation of [[James Inman]] (1821). See J. D. White in ''[[The Nautical Magazine|Nautical Magazine]]'' ([[#White-1926-02|February]] and [[#White-1926-07|July 1926]]).|author-link=Florian Cajori|access-date=2015-11-11|orig-year=1929<!-- 1929-03 -->|author-first=Florian|author-last=Cajori}} (NB. ISBN and link for reprint of 2nd edition by Cosimo, Inc., New York, USA, 2013.)</ref><ref name="Weisstein_covers">{{cite web|url=http://mathworld.wolfram.com/Coversine.html|title=Coversine|publisher=[[Wolfram Research, Inc.]]|archivedate=2005-11-27|dead-url=no|author-first=Eric W.|author-last=Weisstein|author-link=Eric W. Weisstein|work=[[MathWorld]]|access-date=2015-11-06|archive-url=https://web.archive.org/web/20051127184403/http://mathworld.wolfram.com/Coversine.html}}</ref><ref name="Ludlow_1891">{{cite book|url=https://books.google.com/books/about/Elements_of_Trigonometry_with_Logarithmi.html?id=s7iBAAAAIAAJ|title=Elements of Trigonometry with Logarithmic and Other Tables|date=1891|publisher=[[John Wiley & Sons]]|edition=3|location=Boston, USA|page=33|access-date=2015-12-08|author-first1=Henry Hunt|author-last1=Ludlow|author-first2=Edgar Wales|author-last2=Bass}}</ref><ref name="Wentworth_1903">{{cite book|title=Plane Trigonometry<!-- There are several books by the same author dated 1903 with variations on the title ("Plane Trigonometry", "Plane Trigonometry and Tables", "Plane and Spherical Trigonometry", "Plane Trigonometry", "Surveying and Tables"), some mention a coauthor George Anthony Hill. It is unclear, which book was meant specifically. Florian Cajori called it just "Trigonometry". -->|date=1903|publisher=[[Ginn and Company]]|edition=2|location=Boston, USA|page=5|orig-year=1887|author-first=George Albert|author-last=Wentworth}}</ref><ref name="Kenyon_1913">{{cite book|url=https://books.google.com/books?id=RsxHAAAAIAAJ|title=Trigonometry|date=1913|publisher=[[The Macmillan Company]]|location=New York, USA|pages=8–9|access-date=2015-12-08|author-first1=Alfred Monroe|author-last1=Kenyon|author-first2=Louis|author-last2=Ingold}}</ref> '''cosiv(''&#x3B8;'')'''<ref name="Cauchy_1821" /><ref name="Bradley_2009" /><ref group="nb" name="vercosine vs. coversine" /> or '''cvs(''&#x3B8;'')'''<ref name="Precalc_1999" /><ref name="Cajori_1929" /><ref name="Shaneyfelt" /><ref name="Anderegg_1896">{{cite book|url=https://books.google.com/books/about/Trigonometry.html?id=deZHAAAAIAAJ|title=Trigonometry: For Schools and Colleges|date=1896|publisher=[[Ginn and Company]]|location=Boston, USA|page=10|access-date=2015-12-08|author-first1=Frederick|author-last1=Anderegg|author-first2=Edward Drake|author-last2=Roe<!-- sometimes written Rowe -->}}</ref>

1821 godine, [[Augustin Louis Cauchy|Cauchy]] je koristio termine ''sinus versus'' (''siv'') za versinus i ''cosinus versus'' (''cosiv'') za coversinus.<ref name="Cauchy_1821" /><ref name="Bradley_2009" /><ref group="nb" name="vercosine vs. coversine" />

Jedan period (0 < ''&#x3B8;'' < <math> \frac{\pi}{2}</math>) versinusne ili, češće, haversinuse (ili havercosinuse) talasne forme je također često korišten kod obrade signala i teorije upravljanja kod analize pulsa, zbog toga što postoji gladak prelaz (kontinualan u vrijednosti i nagibu) između nule i jedinice (za haversinus) i nakon toga ponovo u nulu.<ref group="nb" name="hvs" /> U ovakvoj primjeni, naziva se [[Hannova funkcija]] ili [[Uzdignuti kosinusni filter|uzdignuti-kosninusni filter]]. Isto tako, havercosinus se koristi kod [[Raised-cosine distribution|uzdignutih-kosinusnih distribucija]] u [[Vjerovatnoća#Teorija|teoriji vjerovatnoće]] i [[Statistika|statistici]].