Tan

Defined in header <cmath>.

Description

Computes the tangent of num (measured in radians). The library provides overloads of std::tan for all cv-unqualified floating-point types as the type of the parameter num.  (od C++23)
Additional Overloads are provided for all integer types, which are treated as double.  (od C++11)

Declarations

C++23

// 1)
/* floating-point-type */ tan( /* floating-point-type */ num );
// 2)
float tanf( float num );
// 3)
long double tanl( long double num );

Additional Overloads

// 4)
template< class Integer >
double tan ( Integer num );

C++11

// 1)
float tan ( float num );
// 2)
double tan ( double num );
// 3)
long double tan ( long double num );
// 4)
float tanf( float num );
// 5)
long double tanl( long double num );

Additional Overloads

// 6)
template< class Integer >
double tan ( Integer num );

Parameters

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

Return value

If no errors occur, the tangent of num (tan(num)) 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.

The function has mathematical poles at π(1/2 + n); however no common floating-point representation is able to represent π/2 exactly, thus there is no value of the argument for which a pole error occurs.

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

Examples

#include <cerrno>
#include <cfenv>
#include <cmath>
#include <iostream>
 
// #pragma STDC FENV_ACCESS ON
const double pi = std::acos(-1); // or C++20's std::numbers::pi
 
int main()
{
    // typical usage
    std::cout 
        << "tan(1*pi/4) = " 
        << std::tan(1*pi/4) 
        << '\n' // 45°
        << "tan(3*pi/4) = " 
        << std::tan(3*pi/4) 
        << '\n' // 135°
        << "tan(5*pi/4) = " 
        << std::tan(5*pi/4) 
        << '\n' // -135°
        << "tan(7*pi/4) = " 
        << std::tan(7*pi/4) 
        << '\n'; // -45°
 
    // special values
    std::cout 
        << "tan(+0) = " 
        << std::tan(0.0) << '\n'
        << "tan(-0) = " 
        << std::tan(-0.0) << '\n';
 
    // error handling
    std::feclearexcept(FE_ALL_EXCEPT);
 
    std::cout 
        << "tan(INFINITY) = " 
        << std::tan(INFINITY) << '\n';
    if (std::fetestexcept(FE_INVALID))
        std::cout 
            << "FE_INVALID raised\n";
}

Possible Result

tan(1*pi/4) = 1
tan(3*pi/4) = -1
tan(5*pi/4) = 1
tan(7*pi/4) = -1
tan(+0) = 0
tan(-0) = -0
tan(INFINITY) = -nan