Function: sin
Section: transcendental
C-Name: gsin
Prototype: Gp
Description:
 (real):real         mpsin($1)
 (mp):real:prec      gsin($1, $prec)
 (gen):gen:prec      gsin($1, $prec)
Help: sin(x): sine of x.
Doc: sine of $x$.
 Note that, for real $x$, cosine and sine can be obtained simultaneously as
 \bprog
 cs(x) = my(z = exp(I*x)); [real(z), imag(z)];
 @eprog and for general complex $x$ as
 \bprog
 cs2(x) = my(z = exp(I*x), u = 1/z); [(z+u)/2, (z-u)/2];
 @eprog Note that the latter function suffers from catastrophic cancellation
 when $z^{2} \approx \pm1$.
