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tan −1 y = tan −1 (x), sometimes interpreted as arctan(x) or arctangent of x, the compositional inverse of the trigonometric function tangent (see below for ambiguity) tan −1 x = tan −1 (x), sometimes interpreted as (tan(x)) −1 = 1 / tan(x) = cot(x) or cotangent of x, the multiplicative inverse (or reciprocal) of the ...
Auxiliary angles, here called and , are constructed such that = (+) / and = /. Therefore, θ = p + q {\displaystyle \theta =p+q} and φ = p − q {\displaystyle \varphi =p-q} . This allows the two congruent purple-outline triangles A F G {\displaystyle AFG} and F C E {\displaystyle FCE} to be constructed, each with hypotenuse cos q ...
In this table, The first cell in each row gives a symbol; The second is a link to the article that details that symbol, using its Unicode standard name or common alias.
Basis of trigonometry: if two right triangles have equal acute angles, they are similar, so their corresponding side lengths are proportional.. In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) [1] are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.
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In this way, this trigonometric identity involving the tangent and the secant follows from the Pythagorean theorem. The angle opposite the leg of length 1 (this angle can be labeled φ = π/2 − θ) has cotangent equal to the length of the other leg, and cosecant equal to the length of the hypotenuse. In that way, this trigonometric identity ...
tan – tangent function. (Also written as tgn, tg.) tanh – hyperbolic tangent function. TFAE – the following are equivalent. tg – tangent function. (Also written as tan, tgn.) tgn – tangent function. (Also written as tan, tg.) Thm – theorem. Tor – Tor functor. Tr – field trace. tr – trace of a matrix or linear transformation ...
The cognates in the table below share meanings in English and Spanish, but have different pronunciation. Some words entered Middle English and Early Modern Spanish indirectly and at different times. For example, a Latinate word might enter English by way of Old French, but enter Spanish directly from Latin. Such differences can introduce ...