Find the Exact Value arcsin(1/2)

Problem

arcsin(1/2)

Solution

1. Identify the definition of the inverse sine function, where y=arcsin(x) means sin(y)=x for y in the interval [−π/2,π/2]

2. Set up the equation to find the angle y such that sin(y)=1/2

3. Recall the unit circle values or special right triangles where the sine of an angle is 1/2

4. Determine that sin(π/6)=1/2 and π/6 falls within the required range [−π/2,π/2]

Final Answer

arcsin(1/2)=π/6

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