std::cos,std::cosf,std::cosl(3)

NAME
std::cos,std::cosf,std::cosl - std::cos,std::cosf,std::cosl

Synopsis
   Defined in header <cmath>
   float cos ( float num );
   double cos ( double num ); (until C++23)
   long double cos ( long double num );
   /* floating-point-type */ (since C++23)
               cos ( /* floating-point-type */ num ); (constexpr since C++26)
   float cosf( float num ); (1) (2) (since C++11)
                        (constexpr since C++26)
   long double cosl( long double num ); (3) (since C++11)
                        (constexpr since C++26)
   Additional overloads (since C++11)
   Defined in header <cmath>
   template< class Integer > (A) (constexpr since C++26)
   double cos ( Integer num );
   1-3) Computes the cosine of num (measured in radians).
   The library provides overloads of std::cos for all cv-unqualified floating-point
   types as the type of the parameter.
   (since C++23)
   A) Additional overloads are provided for all integer types, which are (since C++11)
   treated as double.

Parameters
   num - floating-point or integer value representing angle in radians

Return value
   If no errors occur, the cosine of num (cos(num)) in the range [-1.0, +1.0], is
   returned.
   The result may have little or no significance if the magnitude of num (until C++11)
   is large.
   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, the result is 1.0.
     * 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,
   but it is defined as a domain error in POSIX.
   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::cos(num) has the same effect as std::cos(static_cast<double>(num)).

Example
// Run this code
 #include <cerrno>
 #include <cfenv>
 #include <cmath>
 #include <iomanip>
 #include <iostream>
 #include <numbers>
 // #pragma STDC FENV_ACCESS ON
 constexpr double pi = std::numbers::pi; // or std::acos(-1) before C++20
 constexpr double your_cos(double x)
 {
     double cos{1}, pow{x};
     for (auto fac{1ull}, n{1ull}; n != 19; fac *= ++n, pow *= x)
         if ((n & 1) == 0)
             cos += (n & 2 ? -pow : pow) / fac;
     return cos;
 }
 int main()
 {
     std::cout << std::setprecision(10) << std::showpos
               << "Typical usage:\n"
               << "std::cos(pi/3) = " << std::cos(pi / 3) << '\n'
               << "your cos(pi/3) = " << your_cos(pi / 3) << '\n'
               << "std::cos(pi/2) = " << std::cos(pi / 2) << '\n'
               << "your cos(pi/2) = " << your_cos(pi / 2) << '\n'
               << "std::cos(-3*pi/4) = " << std::cos(-3 * pi / 4) << '\n'
               << "your cos(-3*pi/4) = " << your_cos(-3 * pi / 4) << '\n'
               << "Special values:\n"
               << "std::cos(+0) = " << std::cos(0.0) << '\n'
               << "std::cos(-0) = " << std::cos(-0.0) << '\n';
     // error handling
     std::feclearexcept(FE_ALL_EXCEPT);
     std::cout << "cos(INFINITY) = " << std::cos(INFINITY) << '\n';
     if (std::fetestexcept(FE_INVALID))
         std::cout << " FE_INVALID raised\n";
 }

Possible output:
 Typical usage:
 std::cos(pi/3) = +0.5
 your cos(pi/3) = +0.5
 std::cos(pi/2) = +6.123233996e-17
 your cos(pi/2) = -3.373452105e-15
 std::cos(-3*pi/4) = -0.7071067812
 your cos(-3*pi/4) = -0.7071067812
 Special values:
 std::cos(+0) = +1
 std::cos(-0) = +1
 cos(INFINITY) = -nan
     FE_INVALID raised

See also
   sin
   sinf computes sine (\({\small\sin{x}}\)sin(x))
   sinl (function)
   (C++11)
   (C++11)
   tan
   tanf computes tangent (\({\small\tan{x}}\)tan(x))
   tanl (function)
   (C++11)
   (C++11)
   acos
   acosf computes arc cosine (\({\small\arccos{x}}\)arccos(x))
   acosl (function)
   (C++11)
   (C++11)
   cos(std::complex) computes cosine of a complex number (\({\small\cos{z}}\)cos(z))
                      (function template)
   cos(std::valarray) applies the function std::cos to each element of valarray
                      (function template)
   C documentation for
   cos