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.Dd February 15, 2017
.Dt CACOS 3
.Os
.Sh NAME
.Nm cacos ,
.Nm cacosf ,
.Nm cacosl ,
.Nm cacosh ,
.Nm cacoshf ,
.Nm cacoshl ,
.Nm casin ,
.Nm casinf ,
.Nm casinl ,
.Nm casinh ,
.Nm casinhf ,
.Nm casinhl ,
.Nm catan  ,
.Nm catanf ,
.Nm catanl ,
.Nm catanh ,
.Nm catanhf ,
.Nm catanhl
.Nd complex inverse trigonometric and hyperbolic functions
.Sh LIBRARY
.Lb libm
.Sh SYNOPSIS
.In complex.h
.Ft double complex
.Fn cacos "double complex z"
.Ft float complex
.Fn cacosf "float complex z"
.Ft long double complex
.Fn cacosl "long double complex z"
.Ft double complex
.Fn cacosh "double complex z"
.Ft float complex
.Fn cacoshf "float complex z"
.Ft long double complex
.Fn cacoshl "long double complex z"
.Ft double complex
.Fn casin "double complex z"
.Ft float complex
.Fn casinf "float complex z"
.Ft long double complex
.Fn casinl "long double complex z"
.Ft double complex
.Fn casinh "double complex z"
.Ft float complex
.Fn casinhf "float complex z"
.Ft long double complex
.Fn casinhl "long double complex z"
.Ft double complex
.Fn catan "double complex z"
.Ft float complex
.Fn catanf "float complex z"
.Ft long double complex
.Fn catanl "long double complex z"
.Ft double complex
.Fn catanh "double complex z"
.Ft float complex
.Fn catanhf "float complex z"
.Ft long double complex
.Fn catanhl "long double complex z"
.Sh DESCRIPTION
The
.Fn cacos ,
.Fn casin ,
and
.Fn catan
functions compute the principal value of the inverse cosine, sine,
and tangent of the complex number
.Fa z ,
respectively.
The
.Fn cacosh ,
.Fn casinh ,
and
.Fn catanh
functions compute the principal value of the inverse hyperbolic
cosine, sine, and tangent.
The
.Fn cacosf ,
.Fn casinf ,
.Fn catanf
.Fn cacoshf ,
.Fn casinhf ,
and
.Fn catanhf
functions perform the same operations in
.Fa float
precision.
The
.Fn cacosl ,
.Fn casinl ,
.Fn catanl
.Fn cacoshl ,
.Fn casinhl ,
and
.Fn catanhl
functions perform the same operations in
.Fa long double
precision.
.Pp
.ds Un \[cu]
There is no universal convention for defining the principal values of
these functions.
The following table gives the branch cuts, and the
corresponding ranges for the return values, adopted by the C language.
.Bl -column ".Sy Function" ".Sy (-\*(If*I, -I) \*(Un (I, \*(If*I)" ".Sy [-\*(Pi/2*I, \*(Pi/2*I]"
.It Sy Function Ta Sy Branch Cut(s) Ta Sy Range
.It cacos Ta (-\*(If, -1) \*(Un (1, \*(If) Ta [0, \*(Pi]
.It casin Ta (-\*(If, -1) \*(Un (1, \*(If) Ta [-\*(Pi/2, \*(Pi/2]
.It catan Ta (-\*(If*I, -i) \*(Un (I, \*(If*I) Ta [-\*(Pi/2, \*(Pi/2]
.It cacosh Ta (-\*(If, 1) Ta [-\*(Pi*I, \*(Pi*I]
.It casinh Ta (-\*(If*I, -i) \*(Un (I, \*(If*I) Ta [-\*(Pi/2*I, \*(Pi/2*I]
.It catanh Ta (-\*(If, -1) \*(Un (1, \*(If) Ta [-\*(Pi/2*I, \*(Pi/2*I]
.El
.Sh SEE ALSO
.Xr ccos 3 ,
.Xr ccosh 3 ,
.Xr complex 3 ,
.Xr cos 3 ,
.Xr math 3 ,
.Xr sin 3 ,
.Xr tan 3
.Sh STANDARDS
These functions conform to
.St -isoC-99 .