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std::sin, std::sinf, std::sinl

Defined in header `<cmath>`
	(1)
float sin ( float num ); double sin ( double num ); long double sin ( long double num );		(until C++23)
/* floating-point-type / sin ( / floating-point-type */ num );		(since C++23) (constexpr since C++26)
float sinf( float num );	(2)	(since C++11) (constexpr since C++26)
long double sinl( long double num );	(3)	(since C++11) (constexpr since C++26)
Additional overloads (since C++11)
Defined in header `<cmath>`
template< class Integer > double sin ( Integer num );	(A)	(constexpr since C++26)

1-3) Computes the sine of num (measured in radians). The library provides overloads of std::sin for all cv-unqualified floating-point types as the type of the parameter. (since C++23)

double

(since C++11)

Parameters

num

floating-point or integer value representing angle in radians

Return value

If no errors occur, the sine of num (sin(num)) in the range [-1, +1], is returned.

The result may have little or no significance if the magnitude of num is large.

(until C++11)

If a domain error occurs, an implementation-defined value is returned (NaN where supported).

If a range error occurs due to underflow, the correct result (after rounding) is returned.

Error handling

Errors are reported as specified in math_errhandling.

If the implementation supports IEEE floating-point arithmetic (IEC 60559),

if the argument is ±0, it is returned unmodified
if the argument is ±∞, NaN is returned and FE_INVALID is raised
if the argument is NaN, NaN is returned

Notes

The case where the argument is infinite is not specified to be a domain error in C (to which C++ defers), but it is defined as a domain error in POSIX.

POSIX also specifies that in case of underflow, num is returned unmodified, and if that is not supported, an implementation-defined value no greater than DBL_MIN, FLT_MIN, and LDBL_MIN is returned.

The additional overloads are not required to be provided exactly as (A). They only need to be sufficient to ensure that for their argument num of integer type, std::sin(num) has the same effect as std::sin(static_cast<double>(num)).

Example

#include <cerrno>
#include <cfenv>
#include <cmath>
#include <iomanip>
#include <iostream>
 
// #pragma STDC FENV_ACCESS ON
 
const double pi = std::acos(-1); // or std::numbers::pi since C++20
 
constexpr double your_sin(double x)
{
    double sin {0}, pow {x};
    for (auto fac {1LLU}, n {1ULL}; n != 20; fac *= ++n, pow *= x)
        if (n & 1)
            sin += (n & 2 ? -pow : pow) / fac;
    return sin;
}
 
int main()
{
    std::cout << std::setprecision(10) << std::showpos
              << "Typical usage:\n"
              << "std::sin(pi/6) = " << std::sin(pi / 6) << '\n'
              << "your sin(pi/6) = " << your_sin(pi / 6) << '\n'
              << "std::sin(pi/2) = " << std::sin(pi / 2) << '\n'
              << "your sin(pi/2) = " << your_sin(pi / 2) << '\n'
              << "std::sin(-3*pi/4) = " << std::sin(-3 * pi / 4) << '\n'
              << "your sin(-3*pi/4) = " << your_sin(-3 * pi / 4) << '\n'
              << "Special values:\n"
              << "std::sin(+0) = " << std::sin(0.0) << '\n'
              << "std::sin(-0) = " << std::sin(-0.0) << '\n';
 
    // error handling
    std::feclearexcept(FE_ALL_EXCEPT);
 
    std::cout << "std::sin(INFINITY) = " << std::sin(INFINITY) << '\n';
    if (std::fetestexcept(FE_INVALID))
        std::cout << "    FE_INVALID raised\n";
}

Possible output:

Typical usage:
std::sin(pi/6) = +0.5
your sin(pi/6) = +0.5
std::sin(pi/2) = +1
your sin(pi/2) = +1
std::sin(-3*pi/4) = -0.7071067812
your sin(-3*pi/4) = -0.7071067812
Special values:
std::sin(+0) = +0
std::sin(-0) = -0
std::sin(INFINITY) = -nan
    FE_INVALID raised