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  2. Hyperbolic functions - Wikipedia

    en.wikipedia.org/wiki/Hyperbolic_functions

    Hyperbolic functions occur in the calculations of angles and distances in hyperbolic geometry. They also occur in the solutions of many linear differential equations (such as the equation defining a catenary), cubic equations, and Laplace's equation in Cartesian coordinates. Laplace's equations are important in many areas of physics, including ...

  3. Inverse hyperbolic functions - Wikipedia

    en.wikipedia.org/wiki/Inverse_hyperbolic_functions

    As functions of a complex variable, inverse hyperbolic functions are multivalued functions that are analytic except at a finite number of points. For such a function, it is common to define a principal value, which is a single valued analytic function which coincides with one specific branch of the multivalued function, over a domain consisting ...

  4. List of integrals of hyperbolic functions - Wikipedia

    en.wikipedia.org/wiki/List_of_integrals_of...

    List of integrals of hyperbolic functions. The following is a list of integrals (anti-derivative functions) of hyperbolic functions. For a complete list of integral functions, see list of integrals. In all formulas the constant a is assumed to be nonzero, and C denotes the constant of integration.

  5. List of trigonometric identities - Wikipedia

    en.wikipedia.org/wiki/List_of_trigonometric...

    Viète. de Moivre. Euler. Fourier. v. t. e. In trigonometry, trigonometric identities are equalities that involve trigonometric functions and are true for every value of the occurring variables for which both sides of the equality are defined. Geometrically, these are identities involving certain functions of one or more angles.

  6. Differentiation of trigonometric functions - Wikipedia

    en.wikipedia.org/wiki/Differentiation_of...

    The differentiation of trigonometric functions is the mathematical process of finding the derivative of a trigonometric function, or its rate of change with respect to a variable. For example, the derivative of the sine function is written sin ′ (a) = cos (a), meaning that the rate of change of sin (x) at a particular angle x = a is given by ...

  7. Trigonometric functions - Wikipedia

    en.wikipedia.org/wiki/Trigonometric_functions

    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. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics ...

  8. Inverse trigonometric functions - Wikipedia

    en.wikipedia.org/.../Inverse_trigonometric_functions

    In mathematics, the inverse trigonometric functions (occasionally also called antitrigonometric, [1] cyclometric, [2] or arcus functions [3]) are the inverse functions of the trigonometric functions, under suitably restricted domains. Specifically, they are the inverses of the sine, cosine, tangent, cotangent, secant, and cosecant functions, [4 ...

  9. George Osborn (mathematician) - Wikipedia

    en.wikipedia.org/wiki/George_Osborn_(Mathematician)

    Then exchange all the cosine and sine terms to cosh and sinh terms. However, for all products or implied products of two sine terms replace it with the negative product of two sinh terms. This is because − i sin ⁡ ( i x ) {\displaystyle -i\sin(ix)} is equivalent to sinh ⁡ ( x ) {\displaystyle \sinh(x)} , so when multiplied to together the ...

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