Evaluate arcsin(-1/2)

Problem

arcsin(−1/2)

Solution

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

2. Set the expression equal to an angle θ such that sin(θ)=−1/2

3. Recall the unit circle values where the sine of an angle is −1/2 within the specified range.

4. Determine that sin(−π/6)=−1/2 because sin(π/6)=1/2 and the sine function is odd.

Final Answer

arcsin(−1/2)=−π/6

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