Hyperbolic Functions Calculator
Result
Hyperbolic Functions
Basic hyperbolic functions:
- sinh(x) = (eˣ - e⁻ˣ)/2
- cosh(x) = (eˣ + e⁻ˣ)/2
- tanh(x) = sinh(x)/cosh(x)
- coth(x) = cosh(x)/sinh(x)
- sech(x) = 1/cosh(x)
- csch(x) = 1/sinh(x)
Inverse Hyperbolic Functions
Inverse hyperbolic functions:
- arcsinh(x) = ln(x + √(x² + 1))
- arccosh(x) = ln(x + √(x² - 1))
- arctanh(x) = ½ ln((1 + x)/(1 - x))
Properties
| Function | Domain | Range |
|---|---|---|
| sinh(x) | (-∞, ∞) | (-∞, ∞) |
| cosh(x) | (-∞, ∞) | [1, ∞) |
| tanh(x) | (-∞, ∞) | (-1, 1) |
| arcsinh(x) | (-∞, ∞) | (-∞, ∞) |
| arccosh(x) | [1, ∞) | [0, ∞) |
| arctanh(x) | (-1, 1) | (-∞, ∞) |
Applications
- Physics: Special relativity and wave equations
- Engineering: Transmission line theory
- Mathematics: Complex analysis
- Architecture: Catenary curves
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