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  2. Hyperbolic functions - Wikipedia

    Also, similarly to how the derivatives of sin(t) and cos(t) are cos(t) and –sin(t) respectively, the derivatives of sinh(t) and cosh(t) are cosh(t) and sinh(t) respectively. Hyperbolic functions are …

  3. Hyperbolic Functions - Math is Fun

    The two basic hyperbolic functions are "sinh" and "cosh": Hyperbolic Sine: sinh(x) = e x − e-x 2 (pronounced "shine") Hyperbolic Cosine: cosh(x) = e x + e-x 2 (pronounced "cosh") They use …

  4. Hyperbolic Functions - sinh, cosh, tanh, coth, sech, csch - Math10

    If x = sinh y, then y = sinh-1 a is called the inverse hyperbolic sine of x. Similarly we define the other inverse hyperbolic functions. The inverse hyperbolic functions are multiple-valued and as …

  5. Introduction to the Hyperbolic Sine Function - Wolfram

    where contains the unit step, real part, imaginary part, and the floor functions.. Sums of two direct functions. The sum of two hyperbolic sine functions can be described by the rule: "the sum of …

  6. Hyperbolic Sine -- from Wolfram MathWorld

    May 22, 2025 · The hyperbolic sine is defined as sinhz=1/2(e^z-e^(-z)). (1) The notation shz is sometimes also used (Gradshteyn and Ryzhik 2000, p. xxix). It is implemented in the Wolfram …

  7. Sinh Calculator | Hyperbolic Sine Function

    This sinh calculator allows you to quickly determine the values of the hyperbolic sine function.

  8. Sinh—Wolfram Language Documentation

    Sinh is the hyperbolic sine function, which is the hyperbolic analogue of the Sin circular function used throughout trigonometry. It is defined for real numbers by letting be twice the area …

  9. Sinh|Definition & Meaning - The Story of Mathematics

    The Sinh function is the hyperbolic counterpart of the Sin circle function, which is utilized throughout trigonometry. Real numbers define it by assuming that the area equals twice the …

  10. Hyperbolic Trigonometric Functions | Brilliant Math & Science Wiki

    \[x = \cosh a = \dfrac{e^a + e^{-a}}{2},\quad y = \sinh a = \dfrac{e^a - e^{-a}}{2}.\] A very important fact is that the hyperbolic trigonometric functions take area as their argument (called "the …

  11. sinh - Hyperbolic sine - MATLAB - MathWorks

    Y = sinh(X) returns the hyperbolic sine of the elements of X. The sinh function operates element-wise on arrays. The function accepts both real and complex inputs.

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