Hyperbolic Functions#
- sinh(x)#
Hyperbolic sine function.
- Parameters:
x (Real) – The value to take the hyperbolic sine of.
- Definition:
\(\sinh(x) = \dfrac{e^x - e^{-x}}{2}\)
- Domain:
\((-\infty, \infty)\)
- Range:
\((-\infty, \infty)\)
- Returns:
The value of \(\sinh(x)\).
- Return type:
Real
- cosh(x)#
Hyperbolic cosine function.
- Parameters:
x (Real) – The value to take the hyperbolic cosine of.
- Definition:
\(\cosh(x) = \dfrac{e^x + e^{-x}}{2}\)
- Domain:
\((-\infty, \infty)\)
- Range:
\([1, \infty)\)
- Returns:
The value of \(\cosh(x)\).
- Return type:
Real
- tanh(x)#
Hyperbolic tangent function.
- Parameters:
x (Real) – The value to take the hyperbolic tangent of.
- Definition:
\(\tanh(x) = \dfrac{\sinh(x)}{\cosh(x)}\)
- Domain:
\((-\infty, \infty)\)
- Range:
\((-1, 1)\)
- Returns:
The value of \(\tanh(x)\).
- Return type:
Real
- asinh(x)#
Hyperbolic arcsine function.
- Parameters:
x (Real) – The value to take the hyperbolic arcsine of.
- Definition:
\(\mathrm{asinh}(x)\), the inverse function of \(\sinh(x)\).
- Domain:
\((-\infty, \infty)\)
- Range:
\((-\infty, \infty)\)
- Returns:
The value of \(\mathrm{asinh}(x)\).
- Return type:
Real
- acosh(x)#
Hyperbolic arccosine function.
- Parameters:
x (Real) – The value to take the hyperbolic arccosine of.
- Definition:
\(\mathrm{acosh}(x)\), the inverse function of \(\cosh(x)\) restricted to \(x \geq 0\).
- Domain:
\([1, \infty)\)
- Range:
\([0, \infty)\)
- Returns:
The value of \(\mathrm{acosh}(x)\).
- Return type:
Real
- atanh(x)#
Hyperbolic arctangent function.
- Parameters:
x (Real) – The value to take the hyperbolic arctangent of.
- Definition:
\(\mathrm{atanh}(x)\), the inverse function of \(\tanh(x)\).
- Domain:
\((-1, 1)\)
- Range:
\((-\infty, \infty)\)
- Returns:
The value of \(\mathrm{atanh}(x)\).
- Return type:
Real