Simplify arcsin( square root of 2)

Problem

arcsin(√(,2))

Solution

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

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

3. Compare the input value √(,2) to the domain boundaries.

4. Determine that since √(,2)≈1.414 which is greater than 1 the value lies outside the valid domain.

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

Final Answer

arcsin(√(,2))=undefined

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