Find the exact value of the real number $y$ if it exists. Do not use a calculator.
\[
y=\sin ^{-1}(-2)
\]
Select the correct answer below and, if necessary, fill in the answer box to complete your choice
A. $y=\sin ^{-1}(-2)=$
(Simplify your answer. Type an exact answer, using $\pi$ as needed. Use integers or fractions for any numbers in the expression.)
B. $\sin ^{-1}(-2)$ does not exist.
Answer
Final Answer: \(\boxed{\sin ^{-1}(-2)\text{ does not exist}}\)
Step 1 ：Find the exact value of the real number \(y\) if it exists. Do not use a calculator.
Step 2 ：\(y=\sin ^{-1}(-2)\)
Step 3 ：Select the correct answer below and, if necessary, fill in the answer box to complete your choice
Step 4 ：The sine function, \(\sin(x)\), only takes on values in the range \([-1, 1]\). Therefore, the inverse sine function, \(\sin^{-1}(x)\), is only defined for values in the range \([-1, 1]\). Since \(-2\) is not in this range, \(\sin^{-1}(-2)\) is undefined.
Step 5 ：Final Answer: \(\boxed{\sin ^{-1}(-2)\text{ does not exist}}\)
