Definition of hyperbolic sines. Meaning of hyperbolic sines. Synonyms of hyperbolic sines

Here you will find one or more explanations in English for the word hyperbolic sines. Also in the bottom left of the page several parts of wikipedia pages related to the word hyperbolic sines and, of course, hyperbolic sines synonyms and on the right images related to the word hyperbolic sines.

Definition of hyperbolic sines

hyperbolic sines
Hyperbolic Hy`per*bol"ic, Hyperbolical Hy`per*bol"ic*al, a. [L. hyperbolicus, Gr. ?: cf. F. hyperbolique.] 1. (Math.) Belonging to the hyperbola; having the nature of the hyperbola. 2. (Rhet.) Relating to, containing, or of the nature of, hyperbole; exaggerating or diminishing beyond the fact; exceeding the truth; as, an hyperbolical expression. ``This hyperbolical epitaph.' --Fuller. Hyperbolic functions (Math.), certain functions which have relations to the hyperbola corresponding to those which sines, cosines, tangents, etc., have to the circle; and hence, called hyperbolic sines, hyperbolic cosines, etc. Hyperbolic logarithm. See Logarithm. Hyperbolic spiral (Math.), a spiral curve, the law of which is, that the distance from the pole to the generating point varies inversely as the angle swept over by the radius vector.

Meaning of hyperbolic sines from wikipedia

- φ{\displaystyle \varphi } into a hyperbolic identity, by expanding it completely in terms of integral powers of sines and cosines, changing sine to sinh and cosine...
- treat Cin as the primary function, and derive Ci in terms of Cin. The hyperbolic sine integral is defined as Shi⁡(x)=∫0xsinh⁡(t)tdt.{\displaystyle \operatorname...
- common use: inverse hyperbolic sine, inverse hyperbolic cosine, inverse hyperbolic tangent, inverse hyperbolic cosecant, inverse hyperbolic secant, and inverse...
- x{\displaystyle x} and y{\displaystyle y}, sine and cosine can be expressed in terms of real sines, cosines, and hyperbolic functions as sin⁡z=sin⁡xcosh⁡y+ico...
- Law of Sines In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to...
- In hyperbolic geometry, a hyperbolic triangle is a triangle in the hyperbolic plane. It consists of three line segments called sides or edges and three...
- hyperbola (/haɪˈpɜːrbələ/ ; pl. hyperbolas or hyperbolae /-liː/ ; adj. hyperbolic /ˌhaɪpərˈbɒlɪk/ ) is a type of smooth curve lying in a plane, defined...
- the second word of دالة زائدية "hyperbolic function") is added to the end of trigonometric functions to express hyperbolic functions. This is similar to...
- The following is a list of integrals (anti-derivative functions) of hyperbolic functions. For a complete list of integral functions, see list of integrals...
- indefinite integrals (antiderivatives) of expressions involving the inverse hyperbolic functions. For a complete list of integral formulas, see lists of integrals...