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

Problem

arccos(sin(π/3))

Solution

1. Evaluate the inner trigonometric function sin(π/3) using the unit circle or special right triangles.

sin(π/3)=√(,3)/2

2. Substitute this value back into the original expression.

arccos(√(,3)/2)

3. Determine the angle θ in the interval [0,π] such that cos(θ)=√(,3)/2

θ=π/6

Final Answer

arccos(sin(π/3))=π/6

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