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

Problem

arccot(−√(,3)/3)

Solution

1. Identify the range of the inverse cotangent function. 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. Rationalize the value to recognize a standard trigonometric ratio. Note that −√(,3)/3 is equivalent to −1/√(,3)

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

5. Apply the sign to find the angle in the correct quadrant. Since the cotangent value is negative and the range is (0,π) the angle must be in the second quadrant.

6. Calculate the final angle using the reference angle.

y=π−π/3

y=(2*π)/3

Final Answer

arccot(−√(,3)/3)=(2*π)/3

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