Find the Exact Value arcsin(-1/2)

Problem

arcsin(−1/2)

Solution

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

2. Recall the unit circle values or trigonometric table for the sine function where sin(θ)=y

3. Determine the angle θ within the interval [−π/2,π/2] such that sin(θ)=−1/2

4. Apply the property sin(−θ)=−sin(θ) to find that since sin(π/6)=1/2 then sin(−π/6)=−1/2

Final Answer

arcsin(−1/2)=−π/6

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