Find the Exact Value arcsin(sin((2pi)/3))

Problem

arcsin(sin((2*π)/3))

Solution

1. Evaluate the inner function sin((2*π)/3) using the unit circle.

sin((2*π)/3)=√(,3)/2

2. Substitute this value back into the inverse sine function.

arcsin(√(,3)/2)

3. Determine the angle θ such that sin(θ)=√(,3)/2 within the restricted range of the arcsine function, which is [−π/2,π/2]

θ=π/3

Final Answer

arcsin(sin((2*π)/3))=π/3

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