std::sin(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)

Metaprogramming library (C++11)

Diagnostics library

General utilities library

Strings library

Containers library

Iterators library

Ranges library (C++20)

Algorithms library

Numerics library

Localizations library

Input/output library

Filesystem library (C++17)

Regular expressions library (C++11)

Concurrency support library (C++11)

Execution support 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)
Floating-point environment (C++11)
Complex numbers
Numeric array (valarray)
Pseudo-random number generation
Factor operations
gcd (C++17)	lcm (C++17)
Interpolations
midpoint (C++20)	lerp (C++20)
Saturation arithmetic
add_sat (C++26) sub_sat (C++26) saturate_cast (C++26)	mul_sat (C++26) div_sat (C++26)
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)
Bit operations
has_single_bit (C++20)     bit_cast (C++20) bit_ceil (C++20) bit_floor (C++20) bit_width (C++20) rotl (C++20) rotr (C++20)	popcount (C++20) countl_zero (C++20) countl_one (C++20) countr_zero (C++20) countr_one (C++20) byteswap (C++23) endian (C++20)

 

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> sin( const complex<T>& z );

Computes complex sine of a complex value z.

Parameters

z

-

complex value

Return value

If no errors occur, the complex sine of z is returned.

Errors and special cases are handled as if the operation is implemented by -i * std::sinh(i * z), where i is the imaginary unit.

Notes

The sine is an entire function on the complex plane, and has no branch cuts.

Mathematical definition of the sine is sin z =

eiz -e-iz

2i

.

Example

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 sine along the real line
    std::cout << "sin" << z << " = " << std::sin(z)
              << " ( sin(1) = " << std::sin(1) << ")\n";
 
    std::complex<double> z2(0.0, 1.0); // behaves like sinh along the imaginary line
    std::cout << "sin" << z2 << " = " << std::sin(z2)
              << " (sinh(1) = " << std::sinh(1) << ")\n";
}

Output:

sin(1.000000,0.000000) = (0.841471,0.000000) ( sin(1) = 0.841471)
sin(0.000000,1.000000) = (0.000000,1.175201) (sinh(1) = 1.175201)

See also

cos(std::complex)	computes cosine of a complex number (\({\small\cos{z}}\)cos(z)) (function template)
tan(std::complex)	computes tangent of a complex number (\({\small\tan{z}}\)tan(z)) (function template)
asin(std::complex) (C++11)	computes arc sine of a complex number (\({\small\arcsin{z}}\)arcsin(z)) (function template)
sinsinfsinl (C++11)(C++11)	computes sine (\({\small\sin{x}}\)sin(x)) (function)
sin(std::valarray)	applies the function std::sin to each element of valarray (function template)
C documentation for csin