usr/src/lib/libm/common_source/sin.3

.TH SIN 3M  "8 May 1985"
.UC 4
.SH NAME
sin, cos, tan, asin, acos, atan, atan2 \- trigonometric functions
.SH SYNOPSIS
.nf
.B #include <math.h>
.PP
.B double sin(x)
.B double x;
.PP
.B double cos(x)
.B double x;
.PP
.B double tan(x)
.B double x;
.PP
.B double asin(x)
.B double x;
.PP
.B double acos(x)
.B double x;
.PP
.B double atan(x)
.B double x;
.PP
.B double atan2(y, x)
.B double y, x;
.fi
.SH DESCRIPTION
.I Sin, cos
and
.I tan
return trigonometric functions of radian arguments.
.PP
.I Asin
returns the arc sin in the range \-\(*p/2 to \(*p/2.
.PP
.I Acos
returns the arc cosine in the range 0 to \(*p.
.PP
.I Atan
returns the arc tangent of
.I x
in the range \-\(*p/2 to \(*p/2.
.PP
.I Atan2
returns
.I atan(y/x)
if
.I x
> 0,
.br
.I sign(y)*(\(*p \- atan(|y/x|))
if
.I x
< 0,
.br
.I zero
if
.I x
=
.I y
= 0 and
.br
.I sign(y)*\(*p/2
if
.I x
= 0 but
.I y
not equal to 0.
.SH SEE ALSO
intro(3M), hypot(3M), sqrt(3M)
.SH DIAGNOSTICS
Arguments of magnitude greater than 1 cause
.I asin
and
.I acos
to return the reserved operand on the VAX;
.I errno
is set to EDOM.
.SH NOTES
.I Atan2
defines
.I atan2(0,0)
=
.I 0
on the VAX despite that previously
.I atan2(0,0)
may have generated an error message.
The reasons for assigning a value to
.I atan2(0,0)
are these:
.IP (1)
Any program that already tests whether
.I y
=
.I x
=
.I 0
before computing
.I atan2(y,x)
will be indifferent to whether
.I atan2(0,0)
=
.I 0
or not.
Any program that expects
.I atan2(0,0)
to be invalid is dubious because the consequence of that
invalidity will vary from one computer system to another.
.IP (2)
The principal use for
.I atan2
is conversion between rectangular (\fIx, y\fR) and polar
(\fIr\fR,
.if n\
\fItheta\fR)
.if t\
\fI\(*h\fR)
coordinates that must satisfy
.br
.I x
=
.I r
\(**
.I cos
.if n\
.I theta
.if t\
\(*h
and
.I y
=
.I r
\(**
.I sin
.if n\
.I theta.
.if t\
\(*h.
Then mapping (\fIx\fR = \fI0\fR, \fIy\fR = \fI0\fR) to
(\fIr\fR = \fI0\fR,
.if n\
.I theta
.if t\
.I \(*h
= \fI0\fR)
without fuss saves a programmer from nuisance tests.
In general, given
.I x
and
.I y
the conversion should be effected by computing
.RS
.I r
=
\fIhypot\fR(\fIx\fR,\fIy\fR)                    ... :=
.if n\
\fIsqrt\fR(\fIx**2\fR+\fIy**2\fR)
.if t\
\fIsqrt\fR(\fIx\u\s82\s10\d\fR+\fIy\u\s82\s10\d\fR)
.br
.if n\
.I theta
.if t\
\(*h
=
.I atan2(y,x).
.RE
.IP (3)
On a machine that conforms to IEEE
.I 754,
the foregoing conversion has to cope with signed
.I zeroes
and
.I infinities.
For that purpose the formula above is compatible
with the following:
.br
if
.I x
\(>=
.I 0
then
.if n\
.I theta
.if t\
\(*h
=
.I 2\(**atan(y/(r\fR+\fIx))
else
.if n\
I theta
.if t\
\(*h
=
.I 2\(**atan((r\-x)/y)
.br
except if
.I r
=
.I 0
then replace
.I x
by
.I copysign(1,x)
here, and if
.I r
is infinite take limits to get a multiple of
.if n\
.I pi/4
.if t\
\(*p/4
for
.if n\
.I theta.
.if t\
\(*h.
.SH AUTHOR
Robert P. Corbett, W. Kahan, Stuart McDonald, Kwok\-Choi Ng