\( \begin{aligned} \text { a) } \quad \sin x & =0 \\ 0 & \leqslant x \\ 0 & \leqslant x \\ 0 & \leqslant 360^{\circ}\end{aligned} \)

The equation \( \sin x = 0 \) is satisfied at specific angles where the sine function crosses the x-axis. In the interval \( 0 \leq x \leq 360^\circ \), this occurs at \( x = 0^\circ \), \( 180^\circ \), and \( 360^\circ \). These angles indicate the points where the corresponding y-values of the sine function are zero. In practical terms, knowing where \( \sin x = 0 \) is essential in various fields such as engineering and physics, especially in analyzing wave functions and oscillations. For instance, these angles can help determine the moments when a pendulum is at rest at its equilibrium positions, playing a crucial role in designing mechanisms and understanding motion in real-world applications.