Find the Exact Value arccot(-6)

Problem

arccot(−6)

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. Determine if the value corresponds to a standard reference angle. The value −6 is not a ratio associated with common angles like 30 45 or 60 (e.g., 1 √(,3) or √(,3)/3.

3. Express the exact value using the inverse function notation. Since −6 is not a standard trigonometric ratio, the exact value is represented by the expression itself or by using the relationship with the inverse tangent function.

4. Apply the identity for negative arguments. For the range (0,π) the identity is arccot(−x)=π−arccot(x) Alternatively, using the inverse tangent relationship for x<0 arccot(x)=π+arctan(1/x)

Final Answer

arccot(−6)=π−arccot(6)

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