std::cosh(std::complex)

 

C++

Compiler support

Freestanding and hosted

Language

Standard library

Standard library headers

Named requirements

Feature test macros (C++20)

Language support library

Concepts library (C++20)

Diagnostics library

Memory management library

Metaprogramming library (C++11)

General utilities library

Containers library

Iterators library

Ranges library (C++20)

Algorithms library

Strings library

Text processing library

Numerics library

Date and time library

Input/output library

Filesystem library (C++17)

Concurrency support library (C++11)

Execution control library (C++26)

Technical specifications

Symbols index

External libraries

 

Numerics library

Common mathematical functions
Mathematical special functions (C++17)
Mathematical constants (C++20)
Basic linear algebra algorithms (C++26)
Data-parallel types (SIMD) (C++26)
Floating-point environment (C++11)
Complex numbers
Numeric array (valarray)
Pseudo-random number generation
Bit manipulation (C++20)
Saturation arithmetic (C++26)
Factor operations
gcd (C++17)	lcm (C++17)
Interpolations
midpoint (C++20)	lerp (C++20)
Generic numeric operations
iota (C++11) ranges::iota (C++23) accumulate inner_product adjacent_difference    partial_sum	reduce (C++17) transform_reduce (C++17) inclusive_scan (C++17) exclusive_scan (C++17) transform_inclusive_scan (C++17) transform_exclusive_scan (C++17)
C-style checked integer arithmetic
ckd_add (C++26) ckd_sub (C++26)	ckd_mul (C++26)

 

std::complex

Member functions
complex::complex complex::operator= complex::real complex::imag	complex::operator+=complex::operator-=complex::operator*=complex::operator/=
Non-member functions
operator+operator- operator+operator-operator*operator/ operator==operator!= (until C++20)   operator<<operator>> get(std::complex) (C++26)	real imag abs arg norm conj proj (C++11) polar operator""ioperator""ifoperator""il (C++14)(C++14)(C++14)
Exponential functions
log   log10   exp
Power functions
pow   sqrt
Trigonometric functions
sin   cos tan asin (C++11) acos (C++11) atan (C++11)
Hyperbolic functions
sinh   cosh tanh asinh (C++11) acosh (C++11) atanh (C++11)
Helper types
tuple_size<std::complex> (C++26)
tuple_element<std::complex> (C++26)

 

Defined in header <complex>
template< class T > complex<T> cosh( const complex<T>& z );		(since C++11)

Computes complex hyperbolic cosine of a complex value z.

Parameters

z

-

complex value

Return value

If no errors occur, complex hyperbolic cosine of z is returned.

Error handling and special values

Errors are reported consistent with math_errhandling.

If the implementation supports IEEE floating-point arithmetic,

• std::cosh(std::conj(z)) == std::conj(std::cosh(z))
• std::cosh(z) == std::cosh(-z)
• If z is (+0,+0), the result is (1,+0)
• If z is (+0,+∞), the result is (NaN,±0) (the sign of the imaginary part is unspecified) and FE_INVALID is raised
• If z is (+0,NaN), the result is (NaN,±0) (the sign of the imaginary part is unspecified)
• If z is (x,+∞) (for any finite non-zero x), the result is (NaN,NaN) and FE_INVALID is raised
• If z is (x,NaN) (for any finite non-zero x), the result is (NaN,NaN) and FE_INVALID may be raised
• If z is (+∞,+0), the result is (+∞,+0)
• If z is (+∞,y) (for any finite non-zero y), the result is +∞cis(y)
• If z is (+∞,+∞), the result is (±∞,NaN) (the sign of the real part is unspecified) and FE_INVALID is raised
• If z is (+∞,NaN), the result is (+∞,NaN)
• If z is (NaN,+0), the result is (NaN,±0) (the sign of the imaginary part is unspecified)
• If z is (NaN,+y) (for any finite non-zero y), the result is (NaN,NaN) and FE_INVALID may be raised
• If z is (NaN,NaN), the result is (NaN,NaN)

where cis(y) is cos(y) + i sin(y).

Notes

Mathematical definition of hyperbolic cosine is cosh z =

ez +e-z

2

.

Hyperbolic cosine is an entire function in the complex plane and has no branch cuts. It is periodic with respect to the imaginary component, with period 2πi.

Examples

Run this code

#include <cmath>
#include <complex>
#include <iostream>
 
int main()
{   
    std::cout << std::fixed;
    std::complex<double> z(1.0, 0.0); / behaves like real cosh along the real line
    std::cout << "cosh" << z << " = " << std::cosh(z)
              << " (cosh(1) = " << std::cosh(1) << ")\n";
 
    std::complex<double> z2(0.0, 1.0); / behaves like real cosine along the imaginary line
    std::cout << "cosh" << z2 << " = " << std::cosh(z2)
              << " ( cos(1) = " << std::cos(1) << ")\n";
}

Output:

cosh(1.000000,0.000000) = (1.543081,0.000000) (cosh(1) = 1.543081)
cosh(0.000000,1.000000) = (0.540302,0.000000) ( cos(1) = 0.540302)

See also

sinh(std::complex)	computes hyperbolic sine of a complex number (\({\small\sinh{z}}\)sinh(z)) (function template)
tanh(std::complex)	computes hyperbolic tangent of a complex number (\({\small\tanh{z}}\)tanh(z)) (function template)
acosh(std::complex) (C++11)	computes area hyperbolic cosine of a complex number (\({\small\operatorname{arcosh}{z}}\)arcosh(z)) (function template)
coshcoshfcoshl (C++11)(C++11)	computes hyperbolic cosine (\({\small\cosh{x}}\)cosh(x)) (function)
cosh(std::valarray)	applies the function std::cosh to each element of valarray (function template)
C documentation for ccosh

Follow Lee on X/Twitter - Father, Husband, Serial builder creating AI, crypto, games & web tools. We are friends :) AI Will Come To Life!

Check out: eBank.nz (Art Generator) | Netwrck.com (AI Tools) | Text-Generator.io (AI API) | BitBank.nz (Crypto AI) | ReadingTime (Kids Reading) | RewordGame | BigMultiplayerChess | WebFiddle | How.nz | Helix AI Assistant