Simplify arccos( square root of 3/2)

Problem

arccos(√(,3)/2)

Solution

1. Identify the goal of the inverse cosine function, which is to find an angle θ in the interval [0,π] such that cos(θ)=√(,3)/2

2. Recall the values of the cosine function for standard angles in the first quadrant of the unit circle.

3. Determine the angle where the cosine value is √(,3)/2 which corresponds to 30 or π/6 radians.

4. Verify that π/6 falls within the restricted range of the arccosine function, [0,π]

Final Answer

arccos(√(,3)/2)=π/6

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