1. The problem asks to evaluate $\sin 2^\circ$, which is the sine of $2$ degrees. 2. Sine of small angles can be evaluated using a calculator or known sine values if available. 3. Using a calculator, $\sin 2^\circ \approx 0.0349$. 4. This means the sine of $2$ degrees is approximately $0.0349$. Final answer: $\sin 2^\circ \approx 0.0349$