Find the Exact Value arccot(( square root of 3)/3)

Problem

arccot(√(,3)/3)

Solution

1. Identify the definition of the inverse cotangent function, where y=arccot(x) implies cot(y)=x for y in the interval (0,π)

2. Rewrite the expression using the relationship between cotangent and tangent, noting that cot(y)=1/tan(y)

3. Substitute the given value into the equation to find y

cot(y)=√(,3)/3

4. Rationalize or simplify the ratio to recognize a standard trigonometric value.

cot(y)=1/√(,3)

5. Determine the angle y in the first quadrant where the tangent is √(,3)

tan(y)=√(,3)

6. Conclude that the angle whose tangent is √(,3) in the interval (0,π) is π/3

Final Answer

arccot(√(,3)/3)=π/3

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