Evaluate 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 trigonometric functions for special angles in the first quadrant of the unit circle.

3. Determine the angle where the sine value is √(,3)/2 which corresponds to 60 or π/3 radians.

4. Verify that π/3 falls within the restricted range [−π/2,π/2]

Final Answer

arcsin(√(,3)/2)=π/3

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