SIN(3M)SIN(3M)NAME
sin, cos, tan, asin, acos, atan, atan2 - trigonometric functions and
their inverses
SYNOPSIS
#include <math.h>
double sin(double x);
double cos(double x);
double tan(double x);
double asin(double x);
double acos(double x);
double atan(double x);
double atan2(double y, double x);
DESCRIPTION
Sin, cos and tan return trigonometric functions of radian arguments x.
Asin returns the arc sine in the range -pi/2 to pi/2.
Acos returns the arc cosine in the range 0 to
Atan returns the arc tangent in the range -pi/2 to pi/2.
Atan2 computes the principal value of the arc tangent of y/x, using the
signs of both arguments to determine the quadrant of the return value.
The arc tangent returned is in the range [- pi , + pi ]
ERROR (due to roundoff, etc.)
Let P stand for the number stored in the computer in place of pi =
3.14159 26535 89793 23846 26433 ... . Let “trig” stand for one of
“sin”, “cos” or “tan”. Then the expression “trig(x)” in a program
actually produces an approximation to trig(x∗pi/P), and “atrig(x)”
approximates (P/pi)∗atrig(x). The approximations are close.
In the codes that run on other machines, P differs from pi by a
fraction of an ulp; the difference matters only if the argument x is
huge, and even then the difference is likely to be swamped by the
uncertainty in x. Besides, every trigonometric identity that does not
involve pi explicitly is satisfied equally well regardless of whether P
= pi. For instance, sin(x)**2+cos(x)**2 = 1 and
sin(2x) = 2sin(x)cos(x) to within a few ulps no matter how big x may
be. Therefore the difference between P and pi is most unlikely to
affect scientific and engineering computations.
SEE ALSOmath(3M), hypot(3M), sinh(3M), sqrt(3M)AUTHOR
Robert P. Corbett, W. Kahan, Stuart I. McDonald, Peter Tang and, for
the codes for IEEE 754, Dr. Kwok-Choi Ng.
4th Berkeley Distribution August 1, 1992 SIN(3M)
