Update

sin.md

@@ -178,3 +178,39 @@ int sinInt(int x)
   return sign * (16 * x) / ((5 * PI * PI - 4 * x) / UNIT);
 }
 ```
+
+Mainstream way of implementing [floating point](float.md) sine (but potentially fixed point too) is through [Taylor series](taylor_series.md), i.e. with a [polynomial](polynomial.md) of order *N* that has first *N* [derivatives](derivative.md) identical to the approximated function near some given point. For *sin(x)* near *x = 0* this series is:
+
+*sin(x) = x/1! - x^(3)/3! + x^(5)/5! - x^(7)/7! + ...*
+
+Here is a simple implementation using fixed number of terms, which nonetheless gives quite precise results:
+
+```
+double sinF(double x)
+{
+#define _PI 3.141593
+  if (x < 0)
+    x = -1 * x + _PI;
+
+  int part = (2 * x) / _PI;
+
+  x -= part * _PI / 2;
+
+  if (part % 2)
+    x = _PI / 2 - x;
+#undef _PI
+
+  double x2 = x * x, r = x;
+
+  x *= x2;
+  r -= x / 6;
+  x *= x2;
+  r += x / 120;
+  x *= x2;
+  r -= x / 5040;
+  x *= x2;
+  r += x / 362880;
+  return r;
+}
+```
+