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

Problem

arccot(−√(,3)/3)

Solution

1. Identify the range of the inverse cotangent function. By standard convention, the range of y=arccot(x) is (0,π)

2. Rewrite the expression as an equation. Let y=arccot(−√(,3)/3) which implies cot(y)=−√(,3)/3 for y∈(0,π)

3. Relate the value to sine and cosine. Since cot(y)=cos(y)/sin(y) we look for an angle where the ratio of cosine to sine is −√(,3)/3 which is equivalent to −1/√(,3)

4. Determine the reference angle. We know that cot(π/3)=1/√(,3)=√(,3)/3

5. Find the angle in the correct quadrant. Since the value is negative and the range is (0,π) the angle must be in the second quadrant.

6. Calculate the final value using the reference angle.

y=π−π/3

y=(2*π)/3

Final Answer

arccot(−√(,3)/3)=(2*π)/3

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