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

[edit]Parameters

[edit]Return value

If no errors occur, complex arc cosine ofz 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 withmath_errhandling.

If the implementation supports IEEE floating-point arithmetic,

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