Find the Exact Value arcsin(( square root of 3)/2)

Problem

arcsin(√(,3)/2)

Solution

1. Identify the definition of the inverse sine function, which asks for an angle θ in the interval [−π/2,π/2] such that sin(θ)=√(,3)/2

2. Recall the values of the sine function for standard angles within the unit circle.

3. Determine that sin(π/3)=√(,3)/2 and π/3 falls within the required range [−π/2,π/2]

Final Answer

arcsin(√(,3)/2)=π/3

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