NAME

sin, cos, tan, asin, acos, atan, atan2 − trigonometric functions

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);

void sincos(double x, double ∗s, double ∗c);

double sind(double x);

double cosd(double x);

double tand(double x);

double asind(double x);

double acosd(double x);

double atand(double x);

double atan2d(double y, double x);

void sincosd(double x, double ∗s, double ∗c);

double sinp(double x);

double cosp(double x);

double tanp(double x);

double asinp(double x);

double acosp(double x);

double atanp(double x);

void sincosp(double x, double ∗s, double ∗c);

double sinpi(double x);

double cospi(double x);

double tanpi(double x);

double asinpi(double x);

double acospi(double x);

double atanpi(double x);

double atan2pi(double y, double x);

void sincospi(double x, double ∗s, double ∗c);

DESCRIPTION

sin(x), cos(x), sincos(x,s,c) and tan(x) return trigonometric functions of radian arguments.  Trigonometric argument reduction is discussed in the Floating-Point Programmer’s Guide.  Note that sincos(x,s,c) allows simultaneous computation of ∗s:=sin(x) and ∗c:=cos(x).

asin(x) returns the arc sine of x in the range −π/2 to π/2. 

acos(x) returns the arc cosine of x in the range 0 to π. 

atan(x) returns the arc tangent of x in the range −π/2 to π/2. 

atan2(y,x) and hypot(x,y) (see hypot(3M)) convert rectangular coordinates (x,y) to polar (r,θ); atan2(y,x) computes θ, the argument or phase, by computing an arc tangent of y/x in the range −π to π.  atan2(0.0,0.0) is 0.0, in conformance with SVID. 

sind(x), cosd(x), and tand(x) return trigonometric functions of degree arguments.  sind(x):= sin(x∗π/180). The corresponding inverse functions compute asind(x):= asin(x)∗180/π.  Similarly atan2d(y,x):= atan2(y,x)∗180/π. 

sinpi(x), cospi(x), and tanpi(x) avoid range-reduction issues because their definition sinpi(x):= sin(π∗x) permits range reduction that is fast and exact for all x.  The corresponding inverse functions compute asinpi(x):= asin(x)/π. Similarly atan2pi(y,x):= atan2(y,x)/π. 

sinp(x), cosp(x), and tanp(x) use PI/2, the double precision approximation to π/2, in the argument reduction step to reduce arguments exceeding PI/4 in magnitude to the range −PI/4 to PI/4 .  The argument reduction step is accomplished by the fmod function; thus it is much faster than using the true value of π.  The relation between sinp and sin is sinp(x):= sin(x∗π/PI). The corresponding inverse functions asinp(x):= asin(x)∗PI/π. Since PI/π is close to 1, we simply return asin(x). The same applies to acosp(x) and atanp(x).

DIAGNOSTICS

These functions handle exceptional arguments in the spirit of ANSI/IEEE Std 754-1985 and in conformance with SVID.  sin(±∞), cos(±∞) and tan(±∞) return NaN; asin(x) or acos(x) with |x|>1, return 0.0; sinpi(x) et. al. are similar.  In addition, asin(x), acos(x), and atan2(y,x) may also set errno and call matherr(3M). 

SEE ALSO

hypot(3M), matherr(3M). 

Sun Release 4.1  —  Last change: 25 October 1991