(libc.info.gz) Trig Functions

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 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 |  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 |  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 |  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 |  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 |  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 |  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 |  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.
 

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