sin.3m

来自「<B>Digital的Unix操作系统VAX 4.2源码</B>」· 3M 代码 · 共 172 行

.TH sin 3m RISC
.de Pi		\" PI stuff sign
.if n \\
\\$2pi\\$1
.if t \\
\\$2\\(*p\\$1
..
.ds up \fIulp\fR
.ds nn \fINaN\fR
.SH Name
sin, cos, tan, asin, acos, atan, atan2 \- trigonometric functions
and their inverses
.SH Syntax
.nf
.B #include <math.h>
.PP
.B double sin(\fIx\fP)
.B double \fIx\fP;
.PP
.B float fsin(\fIx\fP)
.B float \fIx\fP;
.PP
.B double cos(\fIx\fP)
.B double \fIx\fP;
.PP
.B float fcos(\fIx\fP)
.B float \fIx\fP;
.PP
.B double tan(\fIx\fP)
.B double \fIx\fP;
.PP
.B float ftan(\fIx\fP)
.B float \fIx\fP;
.PP
.B double asin(\fIx\fP)
.B double \fIx\fP;
.PP
.B float fasin(\fIx\fP)
.B float \fIx\fP;
.PP
.B double acos(\fIx\fP)
.B double \fIx\fP;
.PP
.B float facos(\fIx\fP)
.B float \fIx\fP;
.PP
.B double atan(\fIx\fP)
.B double \fIx\fP;
.PP
.B float fatan(\fIx\fP)
.B float \fIx\fP;
.PP
.B double atan2(\fIy,x\fP)
.B double \fIy,x\fP;
.PP
.B float fatan2(\fIy,x\fP)
.B float \fIy,x\fP;
.fi
.SH Description
.NXR "sin subroutine"
.NXR "cos subroutine"
.NXR "tan subroutine"
.NXR "asin subroutine"
The
.PN sin , 
.PN cos ,
and 
.PN tan
functions return trigonometric functions of radian arguments
.I x
for double data types. 
.PP
The
.PN fsin ,
.PN fcos ,
and
.PN ftan
functions return trigonometric functions for float data types.
.PP
The
.PN asin
and
.PN fasin
functions return the arc sine in the range 
.Pi /2 \-
to
.Pi /2
for double and float data types, respectively.
.PP
.NXR "acos subroutine"
.NXR "atan subroutine"
.NXR "atan2 subroutine"
The 
.PN acos
and
.PN facos
functions return the arc cosine in the range 0 to
.Pi
for double and float data types, respectively.
.PP
The 
.PN atan 
and
.PN fatan
functions return the arc tangent in the range
.Pi /2 \-
to
.Pi /2
for double and float data types, respectively.
.PP
The 
.PN atan2
and
.PN fatan2
functions return the arc tangent of
.I y/x
in the range
.Pi \| \-
to
.Pi,
using the signs of both arguments to determine the quadrant of the return value
for double and float data types, respectively.
.SS Error (due to roundoff)
When
.I P
stands for the number stored in the computer in place of
.Pi " = 3.14159 26535 89793 23846 26433 ... ."
and "trig" stands for one of "sin", "cos" or "tan", then
the expression "trig(\fIx\fP)" in a program actually produces an approximation to
.Pi /P), trig(\fIx\fP\(**
and "atrig(\fIx\fP)" approximates
.Pi )\(**atrig(\fIx\fP). (P/
The approximations are close.
.PP 
P differs from
.Pi
by a fraction of an \*(up; the difference is apparent only if the argument
.I x
is huge, and even then the difference is likely to be swamped by
the uncertainty in
.I x.
Every trigonometric identity that does not involve
.Pi
explicitly is satisfied equally well regardless of whether
.Pi . "P = "
For example,
.if n \
sin(\fIx\fP)**2+cos(\fIx\fP)**2\0=\01
.if t \
sin\u\s62\s10\d(\fIx\fP)+cos\u\s62\s10\d(\fIx\fP)\0=\01
and sin(2\fIx\fP)\0=\02\|sin(\fIx\fP)cos(\fIx\fP) to within a few \*(ups regardless of how big
.I x
is.  Therefore, the difference between P and
.Pi
is unlikely to effect scientific and engineering computations.
.SH Return Values
All the double functions return \*(nn if \*(nn is passed in.
.PP
If |\|x| > 1 then
.PN asin
(\fIx\fP) and
.PN acos
(\fIx\fP) will return the default quiet \*(nn.
.PP
The
.PN atan2
function defines
.PN atan2
(0,0) = \*(nn.
.SH See Also
hypot(3m), math(3m), sqrt(3m)