Next: Inverse Trig Functions, Previous: Mathematical Constants, Up: Mathematics

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)
```

.

— Function: double **sin** (`double x`)

— Function: floatsinf(float x)

— Function: long doublesinl(long double x)

These functions return the sine of

x, wherexis given in radians. The return value is in the range`-1`

to`1`

.

— Function: double **cos** (`double x`)

— Function: floatcosf(float x)

— Function: long doublecosl(long double x)

These functions return the cosine of

x, wherexis given in radians. The return value is in the range`-1`

to`1`

.

— Function: double **tan** (`double x`)

— Function: floattanf(float x)

— Function: long doubletanl(long double x)

These functions return the tangent of

x, wherexis given in radians.Mathematically, the tangent function has singularities at odd multiples of pi/2. If the argument

xis 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.

— Function: void **sincos** (`double x, double *sinx, double *cosx`)

— Function: voidsincosf(float x, float *sinx, float *cosx)

— Function: voidsincosl(long double x, long double *sinx, long double *cosx)

These functions return the sine of

xin`*`

sinxand the cosine ofxin`*`

cos, wherexis given in radians. Both values,`*`

sinxand`*`

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.)

— Function: complex double **csin** (`complex double z`)

— Function: complex floatcsinf(complex float z)

— Function: complex long doublecsinl(complex long double z)

These functions return the complex sine of

z. The mathematical definition of the complex sine issin (z) = 1/(2*i) * (exp (z*i) - exp (-z*i)).

— Function: complex double **ccos** (`complex double z`)

— Function: complex floatccosf(complex float z)

— Function: complex long doubleccosl(complex long double z)

These functions return the complex cosine of

z. The mathematical definition of the complex cosine iscos (z) = 1/2 * (exp (z*i) + exp (-z*i))

— Function: complex double **ctan** (`complex double z`)

— Function: complex floatctanf(complex float z)

— Function: complex long doublectanl(complex long double z)

These functions return the complex tangent of

z. The mathematical definition of the complex tangent istan (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 ifzis too close to a pole.