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# Sinh

 Sinh[z]gives the hyperbolic sine of z.
• Mathematical function, suitable for both symbolic and numerical manipulation.
• For certain special arguments, Sinh automatically evaluates to exact values.
• Sinh can be evaluated to arbitrary numerical precision.
• Sinh automatically threads over lists.
Evaluate numerically:
 Scope   (10)
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:
Sinh can deal with real-valued intervals:
Infinite arguments give symbolic results:
Sinh can be applied to power series:
 Applications   (5)
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:
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