Simplify arccot(- square root of 3)

Problem

arccot(−√(,3))

Solution

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

2. Set up the equation to find the angle θ such that cot(θ)=−√(,3) within the interval (0,π)

3. Relate the cotangent function to sine and cosine to solve for θ

cot(θ)=cos(θ)/sin(θ)=−√(,3)

4. Determine the reference angle. We know that cot(π/6)=√(,3)

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

θ=π−π/6

6. Calculate the final value.

θ=(5*π)/6

Final Answer

arccot(−√(,3))=(5*π)/6

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