Functions {hyperbolic function, trigonometry} can relate to unit hyperbola as trigonometric functions relate to unit circle. For independent variable x and base e of natural logarithms, (e^x - e^-x) / 2 {hyperbolic sine} (sinh). (e^x + e^-x) / 2 {hyperbolic cosine} (cosh). (e^x - e^-x) / (e^x + e^-x) {hyperbolic tangent} (tanh). (e^x + e^-x) / (e^x - e^-x) {hyperbolic cotangent} (coth). 2 / (e^x + e^-x) {hyperbolic secant} (sech). 2 / (e^x - e^-x) {hyperbolic cosecant} (csch).
relations
(sinh(x))^2 + (cosh(x))^2 = cosh(2*x). (cosh(x))^2 - (sinh(x))^2 = 1. sinh(x + y) = sinh(x) * cosh(y) + cosh(x) * sinh(y). cosh(x + y) = cosh(x) * cosh(y) + sinh(x) * sinh(y). arcsinh(x) = ln(x + (x^2 + 1)^0.5).
Mathematical Sciences>Algebra>Function>Kinds>Trigonometric
3-Algebra-Function-Kinds-Trigonometric
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Date Modified: 2022.0224