Find the exact value of $y$, or state that $y$ is undefined.
\[
y=\sin ^{-1}(-1)
\]
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. $\sin ^{-1}(-1)=\square$
(Simplify your answer. Type an exact answer, using $\pi$ as needed. Use integers or fractions for any numbers in the expression.)
B. The answer is undefined.
Answer
Final Answer: \( \sin ^{-1}(-1)=\boxed{-\frac{\pi}{2}} \)
Step 1 ：The inverse sine function, also known as arcsin, is the inverse function of the sine function. It returns the angle whose sine is a given number. In this case, we are asked to find the angle whose sine is -1.
Step 2 ：The sine function takes on the value -1 at an angle of -π/2 (or -90 degrees) in the unit circle. Therefore, the inverse sine of -1 should be -π/2.
Step 3 ：Final Answer: \( \sin ^{-1}(-1)=\boxed{-\frac{\pi}{2}} \)
