Write the complete ionic equation by separating all strong electrolytes into their ions: \(\mathrm{Na^+(aq) + Cl^-(aq) + Ag^+(aq) + NO_3^-(aq) \rightarrow AgCl(s) + Na^+(aq) + NO_3^-(aq)}\).
Identify the solid precipitate, which is \(\mathrm{AgCl(s)}\), and note that it remains as a compound in the ionic equation because it is not dissociated.
Determine which ions appear unchanged on both sides of the complete ionic equation; these ions do not participate in the formation of the precipitate and are called spectator ions.
Conclude that the spectator ions are \(\mathrm{Na^+}\) and \(\mathrm{NO_3^-}\) because they remain dissolved in solution and do not form the solid precipitate.