## 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.

C++ also provides the following overloaded forms:

```    #include <cmath>
float sin( float arg ); // same as sinf() in C99
long double sin( long double arg ); // same as sinl() in C99```

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