functionssinh
Functionssinh refers to the standard hyperbolic sine function, often represented by sinh. In mathematics and most programming libraries, this function is defined for all real inputs x by sinh(x) = (e^x − e^(−x))/2. It is an odd, strictly increasing function with domain (−∞, ∞) and range (−∞, ∞). It is continuous and differentiable everywhere, with derivative d/dx sinh(x) = cosh(x) and integral ∫ sinh(x) dx = cosh(x) + C.
Key identities include sinh(−x) = −sinh(x) and sinh(x + y) = sinh x cosh y + cosh x sinh y.
In numerical computation, functionssinh is typically evaluated via exponentials. For large |x|, direct evaluation can overflow
Applications of the hyperbolic sine appear in physics (relativistic velocity expressions), engineering (catenary curves), and the
See also asinh, cosh, and exp. Notes: 'functionssinh' is a descriptive name for a function implementing the