Simplify arcsin( square root of 3/2)

Problem

arcsin(√(,3)/2)

Solution

1. Identify the goal of the expression, which is to find the 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 in the first quadrant of the unit circle.

3. Determine that sin(π/3)=√(,3)/2 which corresponds to 60

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

Final Answer

arcsin(√(,3)/2)=π/3

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