Simplify arccot(-1)

Problem

arccot(−1)

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 based on the definition of the inverse function. We are looking for an angle θ such that:

cot(θ)=−1

3. Relate the cotangent function to sine and cosine to find the value within the specified range:

cos(θ)/sin(θ)=−1

4. Determine the angle in the second quadrant (0,π) where the cosine and sine have the same absolute value but opposite signs. This occurs at:

θ=(3*π)/4

5. Verify that the value falls within the interval (0,π) Since 0<(3*π)/4<π the value is correct.

Final Answer

arccot(−1)=(3*π)/4

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