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hyperbolic cosines

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.

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.

- } into a hyperbolic identity, by expanding it completely in terms of integral powers of sines and cosines, changing sine to sinh and cosine to cosh, and...

- mathematics, the inverse hyperbolic functions are the inverse functions of the hyperbolic functions. For a given value of a hyperbolic function, the corresponding...

- In hyperbolic geometry, the "law of cosines" is a pair of theorems relating the sides and angles of triangles on a hyperbolic plane, analogous to the planar...

- {cosh(adjacent)}}={\frac {\cos B}{\sin A}}} . The hyperbolic cosine of the hypotenuse is the product of the hyperbolic cosines of the legs. cosh(hypotenuse) = cosh(adjacent)...

- {\displaystyle \operatorname {Si} (ix)=i\operatorname {Shi} (x).} The hyperbolic cosine integral is Chi ( x ) = γ + ln x + ∫ 0 x cosh t − 1 t d t ...

- law of cosines (also known as the cosine formula, cosine rule, or al-Kashi's theorem) relates the lengths of the sides of a triangle to the cosine of one...

- where cosh is the hyperbolic cosine. This formula is a special form of the hyperbolic law of cosines that applies to all hyperbolic triangles: cosh ...

- The following is a list of integrals (anti-derivative functions) of hyperbolic functions. For a complete list of integral functions, see list of integrals...

- x} and y {\displaystyle y} , sine and cosine can be expressed in terms of real sines, cosines, and hyperbolic functions as sin z = sin x cosh y...

- indefinite integrals (antiderivatives) of expressions involving the inverse hyperbolic functions. For a complete list of integral formulas, see lists of integrals...

- mathematics, the inverse hyperbolic functions are the inverse functions of the hyperbolic functions. For a given value of a hyperbolic function, the corresponding...

- In hyperbolic geometry, the "law of cosines" is a pair of theorems relating the sides and angles of triangles on a hyperbolic plane, analogous to the planar...

- {cosh(adjacent)}}={\frac {\cos B}{\sin A}}} . The hyperbolic cosine of the hypotenuse is the product of the hyperbolic cosines of the legs. cosh(hypotenuse) = cosh(adjacent)...

- {\displaystyle \operatorname {Si} (ix)=i\operatorname {Shi} (x).} The hyperbolic cosine integral is Chi ( x ) = γ + ln x + ∫ 0 x cosh t − 1 t d t ...

- law of cosines (also known as the cosine formula, cosine rule, or al-Kashi's theorem) relates the lengths of the sides of a triangle to the cosine of one...

- where cosh is the hyperbolic cosine. This formula is a special form of the hyperbolic law of cosines that applies to all hyperbolic triangles: cosh ...

- The following is a list of integrals (anti-derivative functions) of hyperbolic functions. For a complete list of integral functions, see list of integrals...

- x} and y {\displaystyle y} , sine and cosine can be expressed in terms of real sines, cosines, and hyperbolic functions as sin z = sin x cosh y...

- indefinite integrals (antiderivatives) of expressions involving the inverse hyperbolic functions. For a complete list of integral formulas, see lists of integrals...

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