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

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

Options:

  1. 0
  2. π/2
  3. π
  4. undefined

Correct Answer: π/2

Solution: 

cot^(-1)(0) = π/2

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

Practice Questions

Q1
What is the principal value of cot^(-1)(0)?
  1. 0
  2. π/2
  3. π
  4. undefined

Questions & Step-by-Step Solutions

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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