std::acos(std::complex)

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

[edit] Parameters

[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.

For any z, acos(z) = π - acos(-z).

[edit] Example

#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';
}

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

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