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Trigonometric functions and their reciprocals on the unit circle. All of the right-angled triangles are similar, i.e. the ratios between their corresponding sides are the same. For sin, cos and tan the unit-length radius forms the hypotenuse of the triangle that defines them.
The other four trigonometric functions (tan, cot, sec, csc) can be defined as quotients and reciprocals of sin and cos, except where zero occurs in the denominator. It can be proved, for real arguments, that these definitions coincide with elementary geometric definitions if the argument is regarded as an angle in radians. [ 5 ]
The first published English grammar was a Pamphlet for Grammar of 1586, written by William Bullokar with the stated goal of demonstrating that English was just as rule-based as Latin. Bullokar's grammar was faithfully modeled on William Lily's Latin grammar, Rudimenta Grammatices (1534), used in English schools at that time, having been ...
Reverso has been active since 1998, with the aim of providing online translation and linguistic tools to corporate and mass markets. [3] [4] In 2013 it released Reverso Context, a bilingual dictionary tool based on big data and machine learning algorithms. [5] In 2016 Reverso acquired Fleex, a service for learning English via subtitled movies.
Google Translate is a multilingual neural machine translation service developed by Google to translate text, documents and websites from one language into another. It offers a website interface, a mobile app for Android and iOS, as well as an API that helps developers build browser extensions and software applications. [3]
The unabridged Collins English Dictionary was published on the web on 31 December 2011 on CollinsDictionary.com, along with the unabridged dictionaries of French, German, Spanish and Italian. [5] The site also includes example sentences showing word usage from the Collins Bank of English Corpus, word frequencies and trends from the Google ...
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The following table compares the number of languages which the following machine translation programs can translate between. (Moses and Moses for Mere Mortals allow you to train translation models for any language pair, though collections of translated texts (parallel corpus) need to be provided by the user.