Tanh Calculator
This tanh calculator efficiently computes and clearly explains the hyperbolic tangent function.
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.