Answer:
210 degrees
Explanation:
This is the 'arcsin' or 'inverse sine' function. As written,
arcsin (-1/2) is requesting the angle (in degrees) whose sine is -1/2.
Note that because the sine function is defined as (opposite side)/hypotenuse, the following equation is true:
-1 opposite
------ = ------------------- = sin x, where x is an angle in degrees.
2 hypotenuse
If the sine is negative, that means that the angle x lies in either Quadrant III or Quadrant IV. We see that the magnitude of the opposite side is HALF the magnitude of the hypotenuse.
Cycling counterclockwise from the positive x axis, and continuing through Quadrant II into Quadrant III, we get a ray (hypotenuse) that is twice the length of the opposite side. The angle of this ray as measured from the positive x-axis is 180 degrees plus 30 degrees, or 210 degrees.
You can check this by finding sin 210° on a calculator; the result is -1/2, which is what we were given up front.