std::acos(std::complex)
From cppreference.com
Defined in header <complex>
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template< class T > complex<T> acos( const complex<T>& z ); |
(since C++11) | |
Computes complex arc cosine of a complex value z. Branch cuts exist outside the interval [−1, +1] along the real axis.
Contents |
[edit] Parameters
z | - | complex value |
[edit] 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.
[edit] 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)
[edit] 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 |
).
For any z, acos(z) = π - acos(-z).
[edit] 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)
[edit] See also
(C++11) |
computes arc sine of a complex number (arcsin(z)) (function template) |
(C++11) |
computes arc tangent of a complex number (arctan(z)) (function template) |
computes cosine of a complex number (cos(z)) (function template) | |
(C++11)(C++11) |
computes arc cosine (arccos(x)) (function) |
applies the function std::acos to each element of valarray (function template) | |
C documentation for cacos
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