Use a calculator to give the real number value. (Be sure the calculator is in radian mode.) \[ \sin ^{-1}(-0.2210) \] \[ \sin ^{-1}(-0.2210) \approx \] (Round to four decimal places as needed.)

Step 1 ：The problem is asking for the inverse sine (also known as arcsine) of -0.2210. The inverse sine function, denoted as \(\sin^{-1}(x)\) or asin(x), is the inverse of the sine function. It returns the angle whose sine is x. The result is in radians.

Step 2 ：We can use a calculator to calculate this. The result is a negative radian value. This is because the sine function is negative in the third and fourth quadrants of the unit circle, and the inverse sine function returns the angle in the range of -π/2 to π/2. Therefore, the result is in the fourth quadrant.

Step 3 ：The result is approximately -0.2228397046619687.

Step 4 ：We need to round the result to four decimal places as the question asks. The rounded result is -0.2228.

Step 5 ：Final Answer: The real number value of \(\sin^{-1}(-0.2210)\) rounded to four decimal places is \(\boxed{-0.2228}\).