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Trigonometric Functions

These are the familiar sin, cos, and tan functions. The arguments to all of these functions are in units of radians; recall that pi radians equals 180 degrees.

The math library normally defines M_PI to a double approximation of pi. If strict ISO and/or POSIX compliance are requested this constant is not defined, but you can easily define it yourself: 

#define M_PI 3.14159265358979323846264338327

You can also compute the value of pi with the expression acos (-1.0).

double sin (double x) Function
float sinf (float x) Function
long double sinl (long double x) Function
These functions return the sine of x, where x is given in radians. The return value is in the range -1 to 1.

double cos (double x) Function
float cosf (float x) Function
long double cosl (long double x) Function
These functions return the cosine of x, where x is given in radians. The return value is in the range -1 to 1.

double tan (double x) Function
float tanf (float x) Function
long double tanl (long double x) Function
These functions return the tangent of x, where x is given in radians.

Mathematically, the tangent function has singularities at odd multiples of pi/2. If the argument x is too close to one of these singularities, tan will signal overflow.

In many applications where sin and cos are used, the sine and cosine of the same angle are needed at the same time. It is more efficient to compute them simultaneously, so the library provides a function to do that.

void sincos (double x, double *sinx, double *cosx) Function
void sincosf (float x, float *sinx, float *cosx) Function
void sincosl (long double x, long double *sinx, long double *cosx) Function
These functions return the sine of x in *sinx and the cosine of x in *cos, where x is given in radians. Both values, *sinx and *cosx, are in the range of -1 to 1.

This function is a GNU extension. Portable programs should be prepared to cope with its absence.

ISO C99 defines variants of the trig functions which work on complex numbers. The GNU C library provides these functions, but they are only useful if your compiler supports the new complex types defined by the standard. (As of this writing GCC supports complex numbers, but there are bugs in the implementation.)

complex double csin (complex double z) Function
complex float csinf (complex float z) Function
complex long double csinl (complex long double z) Function
These functions return the complex sine of z. The mathematical definition of the complex sine is

sin (z) = 1/(2*i) * (exp (z*i) - exp (-z*i)).

complex double ccos (complex double z) Function
complex float ccosf (complex float z) Function
complex long double ccosl (complex long double z) Function
These functions return the complex cosine of z. The mathematical definition of the complex cosine is

cos (z) = 1/2 * (exp (z*i) + exp (-z*i))

complex double ctan (complex double z) Function
complex float ctanf (complex float z) Function
complex long double ctanl (complex long double z) Function
These functions return the complex tangent of z. The mathematical definition of the complex tangent is

tan (z) = -i * (exp (z*i) - exp (-z*i)) / (exp (z*i) + exp (-z*i))

The complex tangent has poles at pi/2 + 2n, where n is an integer. ctan may signal overflow if z is too close to a pole.