Hyperbolic Functions Calculator
Hyperbolic functions calculator helps you calculate values of functions such as sinh, cosh, and tanh.
sinh x1.1752011936
cosh x1.5430806348
tanh x0.761594156
coth x1.3130352855
sech x0.6480542737
csch x0.8509181282
cosh²x − sinh²x1always exactly 1
Inverse hyperbolic functions
| arsinh x | 0.881373587 |
| arcosh x | 0 |
| artanh x | needs |x| < 1 |
The method
sinh x = (eˣ − e⁻ˣ)/2, cosh x = (eˣ + e⁻ˣ)/2
Hyperbolic, not circular
Where sine and cosine trace a circle, sinh and cosh trace a hyperbola — hence cosh²x − sinh²x = 1 rather than sin² + cos² = 1. The minus sign is the whole difference.
cosh is the shape of a hanging chain or cable — the catenary — which is why these functions turn up in bridge and power-line engineering rather than only in analysis.