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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 with a unit radius, the points (cosh t, sinh t) form the right half of the unit hyperbola.

cosh (x) = ( e x + e -x )/2. sech (x) = 1/cosh (x) = 2/ ( e x + e -x ) tanh (x) = sinh (x)/cosh (x) = ( e x - e -x )/ ( e x + e -x ) coth (x) = 1/tanh (x) = ( e x + e -x)/ ( e x - e -x ) cosh 2 (x) - sinh 2 (x) = 1. tanh 2 (x) + sech 2 (x) = 1. coth 2 (x) - csch 2 (x) = 1. arcsinh (z) = ln ( …

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 natural exponential function e x. And are not the same as sin(x) and cos(x), but a little bit similar: sinh vs sin. cosh vs cos. Catenary

$\cosh \frac{x}{2} = \sqrt{\frac{\cosh x + 1}{2}}$ $\tanh \frac{x}{2} = \pm \sqrt{\frac{\cosh x - 1}{\cosh x + 1}}$ [+ if x > 0, - if x 0] $=\frac{\text{sinh}(x)}{1 + \text{cosh}(x)} = \frac{\text{cosh}(x) - 1}{\text{sinh}(x)}$

solving 2\cosh2x = 13\cosh x - 12 https://math.stackexchange.com/questions/694929/solving-2-cosh2x-13-cosh-x-12 You are correct: the equation has four solutions.

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Use the definition of cosh: cosh(0) = (exp(0) + exp(-0))/2 = 2 / 2 = 1. Use the identity cosh 2 x − sinh 2 x = 1 along with the fact that sinh is an odd function, which implies sinh(0) = 0. Read the answer from the graph of the hyperbolic cosine function. Use an online cosh calculator.

In basic trigonometry computes sine, cosine, tangent, and their reciprocal. Calculates arcsin, arccos, and arctan values inside inverse trigonometric equations. Trigonometric identities solves extremely difficult trigonometric problems. Conversions of Angles converts radian to degree scale.

The two basic hyperbolic functions are sinh and cosh. sinh(x) = (e x − e −x)/2 cosh(x) = (e x + e −x)/2 (From those two we also get the tanh, coth, sech and csch functions.) Here you see how sinh compares to the sine function and cosh compares to the cosine function: