The functions in this section are related to the exponential functions; see the section called “Exponentiation and Logarithms”.
double function>sinh/function> (double x) float function>sinhf/function> (float x) long double function>sinhl/function> (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.
double function>cosh/function> (double x) float function>coshf/function> (float x) long double function>coshl/function> (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.
double function>tanh/function> (double x) float function>tanhf/function> (float x) long double function>tanhl/function> (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.
complex double function>csinh/function> (complex double z) complex float function>csinhf/function> (complex float z) complex long double function>csinhl/function> (complex long double z) These functions return the complex hyperbolic sine of z, defined mathematically as (exp (z) - exp (-z)) / 2.
complex double function>ccosh/function> (complex double z) complex float function>ccoshf/function> (complex float z) complex long double function>ccoshl/function> (complex long double z) These functions return the complex hyperbolic cosine of z, defined mathematically as (exp (z) + exp (-z)) / 2.
complex double function>ctanh/function> (complex double z) complex float function>ctanhf/function> (complex float z) complex long double function>ctanhl/function> (complex long double z) These functions return the complex hyperbolic tangent of z, defined mathematically as csinh (z) / ccosh (z).
double function>asinh/function> (double x) float function>asinhf/function> (float x) long double function>asinhl/function> (long double x) These functions return the inverse hyperbolic sine of x--the value whose hyperbolic sine is x.
double function>acosh/function> (double x) float function>acoshf/function> (float x) long double function>acoshl/function> (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.
double function>atanh/function> (double x) float function>atanhf/function> (float x) long double function>atanhl/function> (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.
complex double function>casinh/function> (complex double z) complex float function>casinhf/function> (complex float z) complex long double function>casinhl/function> (complex long double z) These functions return the inverse complex hyperbolic sine of z--the value whose complex hyperbolic sine is z.
complex double function>cacosh/function> (complex double z) complex float function>cacoshf/function> (complex float z) complex long double function>cacoshl/function> (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.
complex double function>catanh/function> (complex double z) complex float function>catanhf/function> (complex float z) complex long double function>catanhl/function> (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.