Find the Domain arcsin(x)

Problem

domain *arcsin(x)

Solution

1. Identify the definition of the inverse sine function. The function y=arcsin(x) is the inverse of the function y=sin(x) restricted to the interval [−π/2,π/2]

2. Determine the range of the original sine function. For any real number θ the value of sin(θ) is always between −1 and 1 inclusive.

3. Apply the property of inverse functions. The domain of an inverse function is equal to the range of the original (restricted) function.

4. State the inequality for the domain. Since the output of sin(θ) is in the interval [−1,1] the input x for arcsin(x) must satisfy −1≤x≤1

Final Answer

domain *arcsin(x)=[−1,1]

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