Find the Exact Value 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 by letting y=arccot(−1) which implies cot(y)=−1 for y in the interval (0,π)

3. Recall the values of the cotangent function. We know that cot(π/4)=1

4. Determine the angle in the second quadrant where the cotangent is negative. Since cot(y) is negative in the second quadrant and cot(π−θ)=−cot(θ) we calculate y=π−π/4

5. Simplify the expression to find the exact value.

y=(3*π)/4

Final Answer

arccot(−1)=(3*π)/4

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