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