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1.\" Copyright (c) 2006 Apple Computer
2.\"
3.Dd December 11, 2006
4.Dt CASIN 3
5.Os BSD 4
6.Sh NAME
7.Nm casin
8.Nd complex inverse sine function
9.br
10.Nm catan
11.Nd complex inverse tangent function
12.Sh SYNOPSIS
13.Fd #include <complex.h>
14.Ft double complex
15.Fn casin "double complex z"
16.Ft long double complex
17.Fn casinl "long double complex z"
18.Ft float complex
19.Fn casinf "float complex z"
20.Ft double complex
21.Fn catan "double complex z"
22.Ft long double complex
23.Fn catanl "long double complex z"
24.Ft float complex
25.Fn catanf "float complex z"
26.Sh DESCRIPTION
27.Fn casin "z"
28computes the inverse sine of the complex floating-point number
29.Fa z ,
30with branch cuts outside the interval
31.Bq -1, 1
32on the real axis.
33.Pp
34.Fn ctan "z"
35computes the inverse tangent of the complex floating-point number
36.Fa z ,
37with branch cuts outside the interval
38.Bq -i, i
39on the imaginary axis.
40.Pp
41Both functions return values in a strip of the complex plane with unbounded imaginary part, and real part in the interval
42.Bq -Pi/2, Pi/2 .
43.Sh NOTES
44casin and catan are defined in terms of the complex inverse hyperbolic functions as follows:
45.Bd -literal -offset indent
46casin(z) = -i * casinh(i*z),
47.br
48catan(z) = -i * catanh(i*z).
49.Ed
50.Sh SEE ALSO
51.Xr casinh 3
52.Xr catanh 3
53.Xr complex 3
54.Sh STANDARDS
55The
56.Fn casin
57and
58.Fn catan
59functions conform to ISO/IEC 9899:1999(E).