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Hyperbolic Functions

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

double sinh (double x) Function
float sinhf (float x) Function
long double sinhl (long double x) Function
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.

double cosh (double x) Function
float coshf (float x) Function
long double coshl (long double x) Function
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.

double tanh (double x) Function
float tanhf (float x) Function
long double tanhl (long double x) Function
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.

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

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

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

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

double acosh (double x) Function
float acoshf (float x) Function
long double acoshl (long double x) Function
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.

double atanh (double x) Function
float atanhf (float x) Function
long double atanhl (long double x) Function
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.

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

complex double cacosh (complex double z) Function
complex float cacoshf (complex float z) Function
complex long double cacoshl (complex long double z) Function
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.

complex double catanh (complex double z) Function
complex float catanhf (complex float z) Function
complex long double catanhl (complex long double z) Function
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.