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 $π$ as needed. Use integers or fractions for any numbers in the expression.)
B. $\sin^{- 1} (- 2)$ does not exist.

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Final Answer: $\sin^{- 1} (- 2) does not exist$

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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: $\sin^{- 1} (- 2) does not exist$

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