Hyperbolic functions
sinh x = (ex−e−x)/2; cosh x = (ex+e−x)/2.
Hyperbolic functions are the e-based analogues of trig. Defined from exponentials. Identities mirror trig with sign tweaks.
Worked examples
sinh 0 = 0, cosh 0 = 1, tanh 0 = 0.
cosh²x − sinh²x = 1 (the key Pythagorean-style identity).
cosh x + sinh x = ex.
Frequently asked questions
Why ‘hyperbolic’?
Parameterise the unit hyperbola x² − y² = 1 (vs trig parameterising the unit circle).
Inverse hyperbolic?
arsinh, arcosh, artanh. Used in integration.