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Since the function cosh x is even, only even exponents for x occur in its Taylor series. The sum of the sinh and cosh series is the infinite series expression of the exponential function . The following series are followed by a description of a subset of their domain of convergence , where the series is convergent and its sum equals the function.
Graphs of the inverse hyperbolic functions The hyperbolic functions sinh, cosh, and tanh with respect to a unit hyperbola are analogous to circular functions sin, cos, tan with respect to a unit circle. The argument to the hyperbolic functions is a hyperbolic angle measure.
A formula for computing the trigonometric identities for the one-third angle exists, but it requires finding the zeroes of the cubic equation 4x 3 − 3x + d = 0, where is the value of the cosine function at the one-third angle and d is the known value of the cosine function at the full angle.
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The red section on the right, d, is the difference between the lengths of the hypotenuse, H, and the adjacent side, A.As is shown, H and A are almost the same length, meaning cos θ is close to 1 and θ 2 / 2 helps trim the red away.
The even and odd terms of this series provide sums denoting cosh(x) and sinh(x), so that = + . These transcendental hyperbolic functions can be converted into circular functions sine and cosine by introducing (−1) k into the series, resulting in alternating series.
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cosh (mathematical function), hyperbolic cosine, a mathematical function with notation cosh(x)-COSH, a representation of the thiocarboxylic acid functional group in chemistry; Chlorpromazine, an antipsychotic drug; ChromeOS Shell, an operating system designed by Google