Simplify arccot( square root of 3)

Problem

arccot(√(,3))

Solution

1. Identify the definition of the inverse cotangent function. The expression y=arccot(√(,3)) is equivalent to finding an angle y such that cot(y)=√(,3) within the principal range (0,π)

2. Relate the cotangent function to the tangent function using the reciprocal identity.

cot(y)=1/tan(y)

3. Substitute the given value into the identity to solve for tan(y)

1/tan(y)=√(,3)

tan(y)=1/√(,3)

4. Determine the angle y in the first quadrant that satisfies the tangent equation. From the unit circle, we know that tan(π/6)=1/√(,3)

y=π/6

Final Answer

arccot(√(,3))=π/6

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