Find the Exact Value arcsin(sin(-pi/6))

Problem

arcsin(sin(−π/6))

Solution

1. Identify the range of the principal inverse sine function, which is [−π/2,π/2]

2. Evaluate the inner expression sin(−π/6)

3. Determine if the input value −π/6 falls within the restricted range of the inverse sine function.

4. Apply the property arcsin(sin(x))=x if x is in the interval [−π/2,π/2]

5. Conclude that since −π/6 is between −π/2 and π/2 the expression simplifies directly to the input value.

Final Answer

arcsin(sin(−π/6))=−π/6

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