=====sin=====
Syntax:

<code>
    #include <cmath>
    double sin( double arg );
</code>
The function sin returns the sine of ''arg'', where ''arg'' is given in radians. The
return value of sin will be in the range [-1,1]. If ''arg'' is infinite, sin
will return NAN and raise a floating-point exception.

C++ also provides the following overloaded forms:
<code>
    #include <cmath>
    float sin( float arg ); // same as sinf() in C99
    long double sin( long double arg ); // same as sinl() in C99
</code>

One possible way to [[http://en.wikipedia.org/wiki/Small_angle_approximation|approximate the sine function using the Taylor series]] takes advantage of the fact that sin(x) = x - x<sup>3</sup>/3! + x<sup>5</sup>/5! - x<sup>7</sup>/7! + ..., yielding the following code:

<code>
long factrl(int n) {
  long la = 1;
  for( int i = 2; i <= n; i++ ) la *= i;
  return la;
}

float sin2(float x) {
  int i;
  float y=x ,r=x;
  for( int i=0; i < 10; i++ ) {
    y *= -x*x;
    r += 1.0 / factrl( 1+2*(i+1) ) * y;
  }
  return r;
}

float sin(float theta) {
  float sign = 1, x = theta/M_PI;
  if (x < 0.0) {
    sign = -1;
    x = -x;
  }  
  int i = static_cast<int>(x+0.5);
  float a = x-i;
  if( (i-i/2*2) != 0 ) sign = -sign;
  return sign * sin2(a*M_PI);
}
</code>

Related Topics: [[acos]], [[asin]], [[atan]], [[atan2]], [[cos]], [[cosh]], [[sinh]], [[tan]], [[tanh]]