# cacos.3   [plain text]

```.\" Copyright (c) 2006 Apple Computer
.\"
.Dd December 11, 2006
.Dt CACOS 3
.Os BSD 4
.Sh NAME
.Nm cacos
.Nd complex inverse cosine function
.Sh SYNOPSIS
.Ft double complex
.Fn cacos "double complex z"
.Ft long double complex
.Fn cacosl "long double complex z"
.Ft float complex
.Fn cacosf "float complex z"
.Sh DESCRIPTION
.Fn cacos "z"
computes the inverse cosine of the complex floating-point number
.Fa z ,
with branch cuts outside the interval
.Bq -1,1
along the real axis.
.Pp
.Fn cacos
returns values in a strip of the complex plane with unbounded imaginary part, and real part in the interval
.Bq 0, Pi .
.Pp
For all complex floating point numbers z, cacos(conj(z)) = conj(cacos(z)).
.Sh SPECIAL VALUES
The conjugate symmetry of cacos() is used to abbreviate the specification of special values.
.Pp
.Fn cacos "±0 + 0i"
returns Pi/2 - 0i.
.Pp
.Fn cacos "±0 + NaN i"
returns Pi/2 + NaN i.
.Pp
.Fn cacos "x + inf i"
returns Pi/2 - inf i, for finite x.
.Pp
.Fn cacos "x + NaN i"
returns NaN + NaN i, for finite nonzero x.
.Pp
.Fn cacos "-inf + yi"
returns Pi - inf i, for finite positive-signed y.
.Pp
.Fn cacos "inf + yi"
returns 0 - inf i, for finite positive-signed y.
.Pp
.Fn cacos "-inf + inf i"
returns 3Pi/4 - inf i.
.Pp
.Fn cacos "inf + inf i"
returns Pi/4 - inf i.
.Pp
.Fn cacos "±inf + NaN i"
returns NaN + inf i.
.Pp
.Fn cacos "NaN + yi"
returns NaN + NaN i, for finite y.
.Pp
.Fn cacos "NaN + inf i"
returns NaN - inf i.
.Pp
.Fn cacos "NaN + NaN i"
returns NaN + NaN i.
.Sh NOTES