Simplify arccos(( square root of 3)/2)

Problem

arccos(√(,3)/2)

Solution

1. Identify the definition of the inverse cosine function, where y=arccos(x) means cos(y)=x for y in the interval [0,π]

2. Set up the equation to find the angle y such that cos(y)=√(,3)/2

3. Recall the values of trigonometric functions for special angles in the first quadrant.

4. Determine that cos(π/6)=√(,3)/2 which corresponds to 30

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

Final Answer

arccos(√(,3)/2)=π/6

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