Use a calculator to find a decimal approximation for the following trigonometric function. \[ \sin \left(-302^{\circ} 54^{\prime}\right) \] \[ \sin \left(-302^{\circ} 54^{\prime}\right) \approx \] (Round to eight decimal places)

Step 1 ：First, we need to convert the degrees and minutes to decimal degrees. There are 60 minutes in a degree, so we can convert the minutes to degrees by dividing by 60. Then we can add this to the degrees part to get the total in decimal degrees. The calculation is as follows: \(-302 + \frac{54}{60} = -301.1\)

Step 2 ：Next, we need to convert the degrees to radians because the sin function works with radians. We can do this by multiplying the degrees by \(\frac{\pi}{180}\). The calculation is as follows: \(-301.1 \times \frac{\pi}{180} = -5.255186377754926\)

Step 3 ：Finally, we can calculate the sin of the angle. The calculation is as follows: \(\sin(-5.255186377754926) = 0.8562670846003283\)

Step 4 ：We round the result to eight decimal places to get the final answer: \(\boxed{0.85626708}\)