Find the Exact Value arccot(0)

Problem

arccot(0)

Solution

1. Identify the definition of the inverse cotangent function. The expression y=arccot(x) is equivalent to cot(y)=x where the range of the principal value is typically defined as 0<y<π

2. Set up the equation to solve for the angle y

cot(y)=0

3. Rewrite the cotangent function in terms of sine and cosine.

cos(y)/sin(y)=0

4. Determine the value of y within the interval (0,π) where the numerator is zero. The cosine function equals zero when the angle is π/2

cos(y)=0⇒y=π/2

5. Verify that sin(π/2) is not zero to ensure the expression is defined. Since sin(π/2)=1 the value is valid.

Final Answer

arccot(0)=π/2

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