Find the Exact Value arcsin(sin(pi/3))

Problem

arcsin(sin(π/3))

Solution

1. Identify the range of the principal inverse sine function, arcsin(x) which is [−π/2,π/2]

2. Determine if the input angle π/3 falls within this principal range.

3. Compare the values: since −π/2≤π/3≤π/2 the composition arcsin(sin(θ)) simplifies directly to θ

4. Conclude that the inverse function undoes the sine function because the angle is in the restricted domain.

Final Answer

arcsin(sin(π/3))=π/3

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