In mathematics, hyperbolic functions are analogues of the ordinary trigonometric functions, but defined using the hyperbola rather than the circle. Just as the points (cos t, sin t) form a circle …

2020年9月25日 · sinh(-x) = -sinh(x); cosh(-x) = cosh(x); tanh(-x) = -tanh(x). Their ranges of values differ greatly from the corresponding circular functions: cosh(x) has its minimum value of 1 for …

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 …

The inverse hyperbolic functions are multiple-valued and as in the case of inverse trigonometric functions we restrict ourselves to principal values for which they can be considered as single …

1. Hyperbolic trig functions The hyperbolic trig functions are de ned by sinh(t) = e t e 2; cosh(t) = et+ e t 2: (They usually rhyme with ‘pinch’ and ‘posh’.) As you can see, sinh is an odd function, …

Relations to Trigonometric Functions. sinh(z) = -i sin(iz) csch(z) = i csc(iz) cosh(z) = cos(iz) sech(z) = sec(iz) tanh(z) = -i tan(iz) coth(z) = i cot(iz)

The hyperbolic trigonometric functions extend the notion of the parametric equations for a unit circle \((x = \cos t\) and \(y = \sin t)\) to the parametric equations for a hyperbola, which yield …

trigonometric functions are sinhx = X∞ n=0 x2n+1 (2n +1)! coshx = X∞ n=0 x2n (2n)! and converge for all real x. In fact, using complex analysis and letting i = √ −1, we can easily see …

2023年7月28日 · Hyperbolic Cosine (cosh). cosh(x) = (e^x + e^(-x)) / 2. The hyperbolic cosine is an even function and also demonstrates exponential growth as x increases. The other …

2024年11月25日 · Learn the different hyperbolic trigonometric functions, including sine, cosine, and tangent, with their formulas, examples, and diagrams. Also, learn their identities.