Find the Exact Value arcsin(-1)

Problem

arcsin(−1)

Solution

1. Identify the definition of the inverse sine function, y=arcsin(x) which means finding an angle y such that sin(y)=x

2. Determine the restricted range for the inverse sine function, which is [−π/2,π/2]

3. Locate the value −1 on the unit circle within the specified range.

4. Evaluate the angle where the ycoordinate is −1 which occurs at y=−π/2

Final Answer

arcsin(−1)=−π/2

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