std::acos(std::complex) - cppreference.com (original) (raw)

| | | | | -------------------------------------------------------------- | | ------------- | | 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

• 1 Parameters
• 2 Return value
• 3 Error handling and special values
• 4 Notes
• 5 Example
• 6 See also

[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.

The mathematical definition of the principal value of arc cosine is acos z = π + _i_ln(_i_z + √1-z2
).

For any z, acos(z) = π - acos(-z).

[edit] Example

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