Next: Inverse Trigonometric Functions, Previous: Predefined Mathematical Constants, Up: Mathematics [Contents][Index]

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:
*float***sinf***(float*¶`x`) - Function:
*long double***sinl***(long double*¶`x`) - Function:
*_FloatN***sinfN***(_Float*¶`N``x`) - Function:
*_FloatNx***sinfNx***(_Float*¶`N`x`x`) -
Preliminary: | MT-Safe | AS-Safe | AC-Safe | See POSIX Safety Concepts.

These functions return the sine of

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

to`1`

.

- Function:
*double***cos***(double*¶`x`) - Function:
*float***cosf***(float*¶`x`) - Function:
*long double***cosl***(long double*¶`x`) - Function:
*_FloatN***cosfN***(_Float*¶`N``x`) - Function:
*_FloatNx***cosfNx***(_Float*¶`N`x`x`) -
Preliminary: | MT-Safe | AS-Safe | AC-Safe | See POSIX Safety Concepts.

These functions return the cosine of

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

to`1`

.

- Function:
*double***tan***(double*¶`x`) - Function:
*float***tanf***(float*¶`x`) - Function:
*long double***tanl***(long double*¶`x`) - Function:
*_FloatN***tanfN***(_Float*¶`N``x`) - Function:
*_FloatNx***tanfNx***(_Float*¶`N`x`x`) -
Preliminary: | MT-Safe | AS-Safe | AC-Safe | See POSIX Safety Concepts.

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.

- Function:
*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:
*_FloatN***sincosfN***(_Float*¶`N``x`, _Float`N`*`sinx`, _Float`N`*`cosx`) - Function:
*_FloatNx***sincosfNx***(_Float*¶`N`x`x`, _Float`N`x *`sinx`, _Float`N`x *`cosx`) -
Preliminary: | MT-Safe | AS-Safe | AC-Safe | See POSIX Safety Concepts.

These functions return the sine of

`x`in`*`

and the cosine of`sinx``x`in`*`

, where`cosx``x`is given in radians. Both values,`*`

and`sinx``*`

, are in the range of`cosx``-1`

to`1`

.All these functions, including the

`_Float`

and`N``_Float`

variants, are GNU extensions. Portable programs should be prepared to cope with their absence.`N`x

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 float***csinf***(complex float*¶`z`) - Function:
*complex long double***csinl***(complex long double*¶`z`) - Function:
*complex _FloatN***csinfN***(complex _Float*¶`N``z`) - Function:
*complex _FloatNx***csinfNx***(complex _Float*¶`N`x`z`) -
Preliminary: | MT-Safe | AS-Safe | AC-Safe | See POSIX Safety Concepts.

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))*.

- Function:
*complex double***ccos***(complex double*¶`z`) - Function:
*complex float***ccosf***(complex float*¶`z`) - Function:
*complex long double***ccosl***(complex long double*¶`z`) - Function:
*complex _FloatN***ccosfN***(complex _Float*¶`N``z`) - Function:
*complex _FloatNx***ccosfNx***(complex _Float*¶`N`x`z`) -
Preliminary: | MT-Safe | AS-Safe | AC-Safe | See POSIX Safety Concepts.

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))*

- Function:
*complex double***ctan***(complex double*¶`z`) - Function:
*complex float***ctanf***(complex float*¶`z`) - Function:
*complex long double***ctanl***(complex long double*¶`z`) - Function:
*complex _FloatN***ctanfN***(complex _Float*¶`N``z`) - Function:
*complex _FloatNx***ctanfNx***(complex _Float*¶`N`x`z`) -
Preliminary: | MT-Safe | AS-Safe | AC-Safe | See POSIX Safety Concepts.

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.