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### 19.5 Hyperbolic Functions

The functions in this section are related to the exponential functions; see Exponents 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.