1. The problem is to find the value of $\sin 50^\circ$ and verify the given value $-0.262374853$. 2. Recall that the sine function for angles between $0^\circ$ and $180^\circ$ is positive in the first and second quadrants. 3. Since $50^\circ$ is in the first quadrant, $\sin 50^\circ$ should be positive. 4. Using a calculator or sine table, $\sin 50^\circ \approx 0.7660$. 5. The given value $-0.262374853$ is incorrect for $\sin 50^\circ$; it might be a confusion with $\sin 50$ radians or another angle. 6. To check $\sin 50$ radians, convert $50$ radians to degrees: $50 \times \frac{180}{\pi} \approx 2864.79^\circ$. 7. Since sine is periodic with period $360^\circ$, reduce $2864.79^\circ$ modulo $360^\circ$: $2864.79 - 7 \times 360 = 2864.79 - 2520 = 344.79^\circ$. 8. $\sin 344.79^\circ$ is approximately $-0.2624$, matching the given value. Final answer: $\sin 50^\circ \approx 0.7660$, and the value $-0.262374853$ corresponds to $\sin 50$ radians.