Simplify arccot(( square root of 3)/3)

Problem

arccot(√(,3)/3)

Solution

1. Identify the definition of the inverse cotangent function. The expression y=arccot(x) represents the angle y such that cot(y)=x typically restricted to the interval (0,π)

2. Rewrite the input value to a more recognizable form by rationalizing or simplifying.

√(,3)/3=√(,3)/(√(,3)⋅√(,3))

√(,3)/3=1/√(,3)

3. Relate the cotangent value to sine and cosine.

cot(y)=cos(y)/sin(y)=1/√(,3)

4. Determine the angle in the first quadrant where the ratio of cosine to sine matches this value. For y=π/3 (or 60:

cos(π/3)=1/2

sin(π/3)=√(,3)/2

cot(π/3)=(1/2)/(√(,3)/2)=1/√(,3)

Final Answer

arccot(√(,3)/3)=π/3

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