Final answer:
The exact value of sin⁻¹(-4/5) is -π/3. This is because the inverse sine of a negative number within the range of arcsin, which is from -π/2 to π/2, produces a negative angle in the fourth quadrant.
Step-by-step explanation:
To find the exact value of sin⁻¹(-4/5), we need to consider that the inverse sine function, also known as arcsin, gives us the angle whose sine is the given number. Since the range of arcsin is from -π/2 to π/2, the result must be within this range. The sine function is negative in the third and fourth quadrants, but considering the range of arcsin, our solution is in the fourth quadrant. Therefore, we are looking for a negative angle with a sine value of -4/5.
The reference angle with a sine value of 4/5 is π/3 if it were positive. But since the sine value is negative, the angle we seek is -π/3, which corresponds to answer choice b).