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19.5 Hyperbolic Functions

The functions in this section are related to the exponential functions; see 19.4 Exponentiation and Logarithms.

Function: double sinh (double x)
Function: float sinhf (float x)
Function: long double sinhl (long double x)
These functions return the hyperbolic sine of x, defined mathematically as `(exp (x) - exp (-x)) / 2`. They may signal overflow if x is too large.

Function: double cosh (double x)
Function: float coshf (float x)
Function: long double coshl (long double x)
These function return the hyperbolic cosine of x, defined mathematically as `(exp (x) + exp (-x)) / 2`. They may signal overflow if x is too large.

Function: double tanh (double x)
Function: float tanhf (float x)
Function: long double tanhl (long double x)
These functions return the hyperbolic tangent of x, defined mathematically as `sinh (x) / cosh (x)`. They may signal overflow if x is too large.

There are counterparts for the hyperbolic functions which take complex arguments.

Function: complex double csinh (complex double z)
Function: complex float csinhf (complex float z)
Function: complex long double csinhl (complex long double z)
These functions return the complex hyperbolic sine of z, defined mathematically as `(exp (z) - exp (-z)) / 2`.

Function: complex double ccosh (complex double z)
Function: complex float ccoshf (complex float z)
Function: complex long double ccoshl (complex long double z)
These functions return the complex hyperbolic cosine of z, defined mathematically as `(exp (z) + exp (-z)) / 2`.

Function: complex double ctanh (complex double z)
Function: complex float ctanhf (complex float z)
Function: complex long double ctanhl (complex long double z)
These functions return the complex hyperbolic tangent of z, defined mathematically as `csinh (z) / ccosh (z)`.

Function: double asinh (double x)
Function: float asinhf (float x)
Function: long double asinhl (long double x)
These functions return the inverse hyperbolic sine of x---the value whose hyperbolic sine is x.

Function: double acosh (double x)
Function: float acoshf (float x)
Function: long double acoshl (long double x)
These functions return the inverse hyperbolic cosine of x---the value whose hyperbolic cosine is x. If x is less than `1`, `acosh` signals a domain error.

Function: double atanh (double x)
Function: float atanhf (float x)
Function: long double atanhl (long double x)
These functions return the inverse hyperbolic tangent of x---the value whose hyperbolic tangent is x. If the absolute value of x is greater than `1`, `atanh` signals a domain error; if it is equal to 1, `atanh` returns infinity.

Function: complex double casinh (complex double z)
Function: complex float casinhf (complex float z)
Function: complex long double casinhl (complex long double z)
These functions return the inverse complex hyperbolic sine of z---the value whose complex hyperbolic sine is z.

Function: complex double cacosh (complex double z)
Function: complex float cacoshf (complex float z)
Function: complex long double cacoshl (complex long double z)
These functions return the inverse complex hyperbolic cosine of z---the value whose complex hyperbolic cosine is z. Unlike the real-valued functions, there are no restrictions on the value of z.

Function: complex double catanh (complex double z)
Function: complex float catanhf (complex float z)
Function: complex long double catanhl (complex long double z)
These functions return the inverse complex hyperbolic tangent of z---the value whose complex hyperbolic tangent is z. Unlike the real-valued functions, there are no restrictions on the value of z.

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