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Inverse trigonometric functions
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== References== * {{Cite book|editor1-last=Abramowitz|editor1-first=Milton|editor1-link=Milton Abramowitz|editor2-last=Stegun|editor2-first=Irene A.|editor2-link=Irene Stegun|title=Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables|publisher=[[Dover Publications]]|location=New York|isbn=978-0-486-61272-0|year=1972|url=https://archive.org/details/handbookofmathe000abra}} {{reflist |refs = <ref name="Hall_1909">{{cite book|title=Trigonometry|volume=Part I: Plane Trigonometry|author1-first=Arthur Graham|author1-last=Hall|author2-first=Fred Goodrich|author2-last=Frink|date=January 1909|location=Ann Arbor, Michigan, USA|chapter=Chapter II. The Acute Angle [14] Inverse trigonometric functions|publisher=[[Henry Holt and Company]] / Norwood Press / J. S. Cushing Co. - Berwick & Smith Co., Norwood, Massachusetts, USA|publication-place=New York, USA|page=15|chapter-url = https://archive.org/stream/planetrigonometr00hallrich#page/n30/mode/1up|access-date=2017-08-12|quote=[…] {{mono|1=α = arcsin ''m''}}: It is frequently read "[[arc-sine]] ''m''" or "[[anti-sine]] ''m''," since two mutually inverse functions are said each to be the [[anti-function]] of the other. […] A similar symbolic relation holds for the other [[trigonometric function]]s. […] This notation is universally used in Europe and is fast gaining ground in this country. A less desirable symbol, {{mono|1=α = sin{{sup|-1}}''m''}}, is still found in English and American texts. The notation {{mono|1=α = inv sin ''m''}} is perhaps better still on account of its general applicability. […]}}</ref> <ref name=cyclometric>{{cite book|title=Elementarmathematik vom höheren Standpunkt aus: Arithmetik, Algebra, Analysis|volume=1|author-first=Felix|author-last=Klein|author-link=Felix Klein|date=1924<!-- 1927 -->|orig-year=1902<!-- 1908 -->|edition=3rd|publisher=J. Springer|location=Berlin|language=de}} Translated as {{cite book|title=Elementary Mathematics from an Advanced Standpoint: Arithmetic, Algebra, Analysis |author-first=Felix |author-last=Klein |author-link=Felix Klein |display-authors=0 |year=1932 |publisher=Macmillan |isbn=978-0-486-43480-3 |translator-first1=E. R. |translator-last1=Hedrick |translator-first2=C. A. |translator-last2=Noble |url=https://books.google.com/books?id=8KuoxgykfbkC }}</ref> <ref name="arcus">{{cite book|title=Encyclopaedia of Mathematics|title-link=Encyclopedia of Mathematics|author-first=Michiel|author-last=Hazewinkel|author-link=Michiel Hazewinkel|publisher=[[Kluwer Academic Publishers]] / [[Springer Science & Business Media]]|orig-year=1987|date=1994|edition=unabridged reprint|isbn=978-155608010-4}} {{pb}} {{cite book |last1=Bronshtein |first1=I. N. |last2=Semendyayev |first2=K. A. |last3=Musiol |first3=Gerhard |last4=Mühlig |first4=Heiner |title=Handbook of Mathematics |edition=6th |publisher=Springer |location=Berlin |doi=10.1007/978-3-663-46221-8 |chapter=Cyclometric or Inverse Trigonometric Functions |doi-broken-date=1 November 2024 |at={{nobr|§ 2.8}}, {{pgs|85–89}} }} {{pb}} However, the term "arcus function" can also refer to the function giving the [[Argument (complex analysis)|argument]] of a complex number, sometimes called the ''arcus''.</ref> <ref name="Americana_1912">{{cite book|chapter=Inverse trigonometric functions|title=The Americana: a universal reference library|volume=21|editor-first1=Frederick Converse|editor-last1=Beach|editor-first2=George Edwin|editor-last2=Rines|date=1912|title-link=The Americana}}</ref> <ref name="Cajori">{{cite book|url = https://archive.org/details/ahistorymathema02cajogoog|author-last=Cajori|author-first=Florian|author-link=Florian Cajori|title=A History of Mathematics|page=[https://archive.org/details/ahistorymathema02cajogoog/page/n284 272]|edition=2|year=1919|publisher=[[The Macmillan Company]]|location=New York, NY}}</ref> <ref name="Herschel_1813">{{cite journal|url=https://books.google.com/books?id=qpRJAAAAYAAJ&pg=PA8|author-last=Herschel|author-first=John Frederick William|author-link=John Frederick William Herschel|title=On a remarkable Application of Cotes's Theorem|journal=Philosophical Transactions|page=8|volume=103|number=1|date=1813|publisher=Royal Society, London|doi=10.1098/rstl.1813.0005|doi-access=free}}</ref> <ref name="Korn_2000">{{cite book|title=Mathematical handbook for scientists and engineers: Definitions, theorems, and formulars for reference and review|url=https://archive.org/details/mathematicalhand00korn_849|url-access=limited|first1=Grandino Arthur|last1=Korn|first2=Theresa M.|last2=Korn|author2-link= Theresa M. Korn|edition=3<!-- (based on 1968 edition by McGrawHill, Inc.) -->|year=2000|orig-year=1961|publisher=[[Dover Publications, Inc.]]|location=Mineola, New York, USA|chapter=21.2.-4. Inverse Trigonometric Functions|page=[https://archive.org/details/mathematicalhand00korn_849/page/n828 811]|isbn=978-0-486-41147-7}}</ref> <ref name="Bhatti_1999">{{cite book|title=Calculus and Analytic Geometry|date=1999|publisher=Punjab Textbook Board|location=[[Lahore]]|edition=1|page=140|author-first1=Sanaullah|author-last1=Bhatti|author-last2=Nawab-ud-Din|author-first3=Bashir|author-last3=Ahmed|author-first4=S. M.|author-last4=Yousuf|author-first5=Allah Bukhsh|author-last5=Taheem|editor-first1=Mohammad Maqbool|editor-last1=Ellahi|editor-first2=Karamat Hussain|editor-last2=Dar|editor-first3=Faheem|editor-last3=Hussain|language=en-PK|chapter=Differentiation of Trigonometric, Logarithmic and Exponential Functions}}</ref> <ref name="Borwein_2004">{{cite book|title=Experimentation in Mathematics: Computational Paths to Discovery|url=https://archive.org/details/experimentationm00borw_656|url-access=limited|author-first1=Jonathan|author-last1=Borwein|author-first2=David|author-last2=Bailey|author-first3=Roland|author-last3=Gingersohn|edition=1|date=2004|publisher=[[A. K. Peters]]|page=[https://archive.org/details/experimentationm00borw_656/page/n60 51]|location=Wellesley, MA, USA|isbn=978-1-56881-136-9}}</ref> <ref name="Gade_2010">{{cite journal|author-last=Gade|author-first=Kenneth|date=2010|title=A non-singular horizontal position representation|journal=The Journal of Navigation|publisher=[[Cambridge University Press]]|volume=63|issue=3|pages=395–417|url=http://www.navlab.net/Publications/A_Nonsingular_Horizontal_Position_Representation.pdf|doi=10.1017/S0373463309990415|bibcode=2010JNav...63..395G}}</ref> }}
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