Find the Exact Value arcsin(-5)

Problem

arcsin(−5)

Solution

1. Identify the domain of the inverse sine function, arcsin(x)

2. Recall that the domain of arcsin(x) is the interval [−1,1]

3. Compare the given value x=−5 to the domain boundaries.

4. Determine that since −5<−1 the value −5 lies outside the valid domain of the function.

5. Conclude that the expression is undefined in the set of real numbers.

Final Answer

arcsin(−5)=Undefined

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