Let
$$S = \left\{ \left( \theta \sin \frac { \pi \theta } { 1 + \theta } , \frac { 1 } { \theta } \cos \frac { \pi \theta } { 1 + \theta } \right) : \theta \in \mathbb { R } , \theta > 0 \right\}$$
and
$$T = \left\{ ( x , y ) : x \in \mathbb { R } , y \in \mathbb { R } , x y = \frac { 1 } { 2 } \right\}$$
How many elements does $S \cap T$ have?\\
(A) 0\\
(B) 1\\
(C) 2\\
(D) 3