Sinh

Evaluate to high precision:

The precision of the output tracks the precision of the input:

Sinh threads element-wise over lists and matrices:

Sinh can take complex number inputs:

Simple exact purely imaginary values are generated automatically:

Convert multiple-angle expressions:

Convert sums of hyperbolic functions to products:

Expand assuming real variables:

Convert to exponentials:

TraditionalForm formatting:

Sinh can deal with real-valued intervals:

Infinite arguments give symbolic results:

Sinh can be applied to power series:

Draw a hyperbola:

Rotation matrix in hyperbolic space:

Build from infinitesimal transformations:

Relativistic boost matrix:

The matrix is orthogonal with respect to the Minkowski metric:

Construct a relativistic coordinate transformation for rapidity :

Prolate spheroidal coordinates:

Special solution of the Sine-Gordon equation:

Basic parity and periodicity properties of the hyperbolic sine function get automatically applied:

Complicated expressions containing hyperbolic functions do not autosimplify:

Compose with inverse functions:

Solve a hyperbolic equation:

Numerically find a root of a transcendental equation:

Reduce a hyperbolic equation:

Integrals:

Integral transforms:

Sinh appears in special cases of many mathematical functions:

Sinh is a numeric function:

Machine-precision input is insufficient to give a correct answer:

With exact input, the answer is correct:

A larger setting for $MaxExtraPrecision can be needed:

Machine number inputs can give high-precision results:

No power series exists at infinity, where Sinh has an essential singularity:

In traditional form parentheses are needed around the argument:

Nested hyperbolic cosine over the complex plane: