Find the exact value of sin−1−12.Write your answer in radians in terms of π.=sin−1−12

The inverse sine function, sin^(-1)(x), gives the angle whose sine is x.

Here, we are asked to find the angle whose sine is -1/2.

We know that sin(π/6) = 1/2 in the unit circle. However, since the sine value is negative, we are dealing with an angle in the 3rd or 4th quadrant (where sine values are negative).

The reference angle in the 3rd quadrant is π + π/6 = 7π/6.

The reference angle in the 4th quadrant is 2π - π/6 = 11π/6.

However, the range of the inverse sine function is [-π/2, π/2] in the 4th quadrant and [π/2, 3π/2] in the 3rd quadrant.

Therefore, the exact value of sin^(-1)(-1/2) is -π/6 in radians.