NAME¶

std::acos(std::complex) - std::acos(std::complex)

Synopsis¶

Defined in header <complex>
template< class T > (since C++11)
complex<T> acos( const complex<T>& z );

Computes complex arc cosine of a complex value z. Branch cuts exist outside the
interval [−1 ; +1] along the real axis.

Parameters¶

z - complex value

Return value¶

If no errors occur, complex arc cosine of z is returned, in the range of a strip
unbounded along the imaginary axis and in the interval [0; +π] along the real axis.

Error handling and special values

Errors are reported consistent with math_errhandling

If the implementation supports IEEE floating-point arithmetic,

* std::acos(std::conj(z)) == std::conj(std::acos(z))
* If z is (±0,+0), the result is (π/2,-0)
* If z is (±0,NaN), the result is (π/2,NaN)
* If z is (x,+∞) (for any finite x), the result is (π/2,-∞)
* If z is (x,NaN) (for any nonzero finite x), the result is (NaN,NaN) and
FE_INVALID may be raised.
* If z is (-∞,y) (for any positive finite y), the result is (π,-∞)
* If z is (+∞,y) (for any positive finite y), the result is (+0,-∞)
* If z is (-∞,+∞), the result is (3π/4,-∞)
* If z is (+∞,+∞), the result is (π/4,-∞)
* If z is (±∞,NaN), the result is (NaN,±∞) (the sign of the imaginary part
is unspecified)
* If z is (NaN,y) (for any finite y), the result is (NaN,NaN) and FE_INVALID may
be raised
* If z is (NaN,+∞), the result is (NaN,-∞)
* If z is (NaN,NaN), the result is (NaN,NaN)

Notes¶

Inverse cosine (or arc cosine) is a multivalued function and requires a branch cut
on the complex plane. The branch cut is conventionally placed at the line segments
(-∞,-1) and (1,∞) of the real axis.

The mathematical definition of the principal value of arc cosine is acos z =

1
2

π + iln(iz +
√
1-z2
)

For any z, acos(z) = π - acos(-z)

Example¶

// Run this code

#include <iostream>
#include <cmath>
#include <complex>

int main()
{
std::cout << std::fixed;
std::complex<double> z1(-2, 0);
std::cout << "acos" << z1 << " = " << std::acos(z1) << '\n';

std::complex<double> z2(-2, -0.0);
std::cout << "acos" << z2 << " (the other side of the cut) = "
<< std::acos(z2) << '\n';

// for any z, acos(z) = pi - acos(-z)
const double pi = std::acos(-1);
std::complex<double> z3 = pi - std::acos(z2);
std::cout << "cos(pi - acos" << z2 << ") = " << std::cos(z3) << '\n';
}

Output:¶

acos(-2.000000,0.000000) = (3.141593,-1.316958)
acos(-2.000000,-0.000000) (the other side of the cut) = (3.141593,1.316958)
cos(pi - acos(-2.000000,-0.000000)) = (2.000000,0.000000)

See also¶

asin(std::complex) computes arc sine of a complex number (\({\small\arcsin{z}
(C++11) }\)arcsin(z))
(function template)
atan(std::complex) computes arc tangent of a complex number (\({\small\arctan{z}
(C++11) }\)arctan(z))
(function template)
cos(std::complex) computes cosine of a complex number (\({\small\cos{z} }\)cos(z))
(function template)
acos
acosf computes arc cosine (\({\small\arccos{x} }\)arccos(x))
acosl (function)
(C++11)
(C++11)
acos(std::valarray) applies the function std::acos to each element of valarray
(function template)