## Hyperbolic

### sinh function

Returns the hyperbolic sine of the argument.

sinh(z)

#### Description

The `sinh` function calculates the hyperbolic sine of `z`. `z` may be any numeric expression that evaluates to a real number or a complex number.

Hyperbolic sine is defined as: sinh(z) = ½(ez-e-z)

#### See also

 Wikipedia MathWorld

### cosh function

Returns the hyperbolic cosine of the argument.

cosh(z)

#### Description

The `cosh` function calculates the hyperbolic cosine of `z`. `z` may be any numeric expression that evaluates to a real number or a complex number.

Hyperbolic cosine is defined as: cosh(z) = ½(ez+e-z)

#### See also

 Wikipedia MathWorld

### tanh function

Returns the hyperbolic tangent of the argument.

tanh(z)

#### Description

The `tanh` function calculates the hyperbolic tangent of `z`. `z` may be any numeric expression that evaluates to a real number or a complex number.

Hyperbolic tangent is defined as: tanh(z) = sinh(z)/cosh(z)

#### See also

 Wikipedia MathWorld

### asinh function

Returns the inverse hyperbolic sine of the argument.

asinh(z)

#### Description

The `asinh` function calculates the inverse hyperbolic sine of `z`. `z` may be any numeric expression that evaluates to a real number or a complex number. `asinh` is the reverse of `sinh`, i.e. asinh(sinh(z)) = z.

#### See also

 Wikipedia MathWorld

### acosh function

Returns the inverse hyperbolic cosine of the argument.

acosh(z)

#### Description

The `acosh` function calculates the inverse hyperbolic cosine of `z`. `z` may be any numeric expression that evaluates to a real number or a complex number. `acosh` is the reverse of `cosh`, i.e. acosh(cosh(z)) = z.

#### See also

 Wikipedia MathWorld

### atanh function

Returns the inverse hyperbolic tangent of the argument.

atanh(z)

#### Description

The `atanh` function calculates the inverse hyperbolic tangent of `z`. `z` may be any numeric expression that evaluates to a real number or a complex number. `atanh` is the reverse of `tanh`, i.e. atanh(tanh(z)) = z.

#### See also

 Wikipedia MathWorld

### csch function

Returns the hyperbolic cosecant of the argument.

csch(z)

#### Description

The `csch` function calculates the hyperbolic cosecant of `z`. `z` may be any numeric expression that evaluates to a real number or a complex number.

Hyperbolic cosecant is defined as: csch(z) = 1/sinh(z) = 2/(ez-e-z)

#### See also

 Wikipedia MathWorld

### sech function

Returns the hyperbolic secant of the argument.

sech(z)

#### Description

The `sech` function calculates the hyperbolic secant of `z`. `z` may be any numeric expression that evaluates to a real number or a complex number.

Hyperbolic secant is defined as: sech(z) = 1/cosh(z) = 2/(ez+e-z)

#### See also

 Wikipedia MathWorld

### coth function

Returns the hyperbolic cotangent of the argument.

coth(z)

#### Description

The `coth` function calculates the hyperbolic cotangent of `z`. `z` may be any numeric expression that evaluates to a real number or a complex number.

Hyperbolic cotangent is defined as: coth(z) = 1/tanh(z) = cosh(z)/sinh(z) = (ez + e-z)/(ez - e-z)

#### See also

 Wikipedia MathWorld

### acsch function

Returns the inverse hyperbolic cosecant of the argument.

acsch(z)

#### Description

The `acsch` function calculates the inverse hyperbolic cosecant of `z`. `z` may be any numeric expression that evaluates to a real number or a complex number. `acsch` is the reverse of `csch`, i.e. acsch(csch(z)) = z.

#### See also

 Wikipedia MathWorld

### asech function

Returns the inverse hyperbolic secant of the argument.

asech(z)

#### Description

The `asech` function calculates the inverse hyperbolic secant of `z`. `z` may be any numeric expression that evaluates to a real number or a complex number. `asech` is the reverse of `sech`, i.e. asech(sech(z)) = z.

#### See also

 Wikipedia MathWorld

### acoth function

Returns the inverse hyperbolic cotangent of the argument.

acoth(z)

#### Description

The `acoth` function calculates the inverse hyperbolic cotangent of `z`. `z` may be any numeric expression that evaluates to a real number or a complex number. `acoth` is the reverse of `coth`, i.e. acoth(coth(z)) = z. For real numbers `acoth` is undefined in the interval [-1;1].

#### See also

 Wikipedia MathWorld