What is the principal value of cot^(-1)(0)?

What is the principal value of cot^(-1)(0)?

Step 1: Understand what cot^(-1)(0) means. It is asking for the angle whose cotangent is 0.
Step 2: Recall that cotangent is the reciprocal of tangent. So, cot(x) = 1/tan(x).
Step 3: If cot(x) = 0, then tan(x) must be undefined because you cannot divide by zero.
Step 4: The tangent function is undefined at certain angles, specifically at π/2 (90 degrees) and (3π/2) (270 degrees).
Step 5: The principal value of cot^(-1)(0) is the angle in the range of 0 to π (0 to 180 degrees) where cotangent is 0.
Step 6: The angle π/2 is within this range and is the correct answer.

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