c:math:sin

Syntax:

    #include <cmath>
    double sin( double arg );

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.

One possible way to approximate the sine function using the Taylor series takes advantage of the fact that sin(x) = x - x³/3! + x⁵/5! - x⁷/7! + …, yielding the following 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);
}

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