table of contents
std::acos(std::complex)(3) | C++ Standard Libary | std::acos(std::complex)(3) |
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 <cmath>
#include <complex>
#include <iostream>
int main()
{
std::cout << std::fixed;
std::complex<double> z1(-2.0, 0.0);
std::cout << "acos" << z1 << " = "
<< std::acos(z1) << '\n';
std::complex<double> z2(-2.0, -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
(C++11) (\({\small\arcsin{z}}\)arcsin(z))
(function template)
atan(std::complex) computes arc tangent of a complex number
(C++11) (\({\small\arctan{z}}\)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)
C documentation for
cacos
2024.06.10 | http://cppreference.com |