### 19.2 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)`.

— Function: double sin (double x)

> — Function: float sinf (float x)

> > — Function: long double sinl (long double 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)

> > > 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)

> > > 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)

> > > Preliminary: | MT-Safe | AS-Safe | AC-Safe | See POSIX Safety Concepts.

> > > 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.)

— Function: complex double csin (complex double z)

> — Function: complex float csinf (complex float z)

> > — Function: complex long double csinl (complex long double 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)

> > > 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)

> > > 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.