1. Datos del problema:
Sea $u = \sin x$ y $v = \cos y$. El sistema se convierte en:
1) $u + v = 0 \implies v = -u$
2) $u^2 + v^2 = 1/2$

2. Desarrollo paso a paso:
Sustituyendo $v = -u$ en la segunda ecuación:
$$ u^2 + (-u)^2 = \frac{1}{2} \implies 2u^2 = \frac{1}{2} \implies u^2 = \frac{1}{4} $$
Por lo tanto:
$$ u = \pm \frac{1}{2} $$

Caso 1: $u = 1/2$
$$ \sin x = \frac{1}{2} \implies x = (-1)^k \frac{\pi}{6} + k\pi $$
$$ v = -1/2 \implies \cos y = -\frac{1}{2} \implies y = \pm \frac{2\pi}{3} + 2n\pi $$

Caso 2: $u = -1/2$
$$ \sin x = -\frac{1}{2} \implies x = (-1)^k \left(-\frac{\pi}{6}\right) + k\pi $$
$$ v = 1/2 \implies \cos y = \frac{1}{2} \implies y = \pm \frac{\pi}{3} + 2n\pi $$

3. Resultado final:
$$ \boxed{ (x, y) \in \left\{ \left( \frac{\pi}{6}, \frac{2\pi}{3} \right), \left( \frac{5\pi}{6}, \frac{2\pi}{3} \right), \dots \right\} $$