Find the Value Using the Unit Circle 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] or [−90,90]

2. Determine the angle θ within this range such that sin(θ)=−1/2

3. Locate the point on the unit circle where the ycoordinate is −1/2 in the fourth quadrant (specifically between −π/2 and 0.

4. Recall that sin(π/6)=1/2 so for a negative value in the required interval, the angle must be −π/6

Final Answer

arcsin(−1/2)=−π/6

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