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What is the value of cot(cos^(-1)(1/2))?

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Question: What is the value of cot(cos^(-1)(1/2))?

Options:

  1. √3
  2. 1/√3
  3. 2
  4. √2

Correct Answer: √3

Solution: 

cot(cos^(-1)(1/2)) = √3

What is the value of cot(cos^(-1)(1/2))?

Practice Questions

Q1
What is the value of cot(cos^(-1)(1/2))?
  1. √3
  2. 1/√3
  3. 2
  4. √2

Questions & Step-by-Step Solutions

What is the value of cot(cos^(-1)(1/2))?
  • Step 1: Understand the function cos^(-1)(1/2). This means we are looking for an angle whose cosine is 1/2.
  • Step 2: Recall that cos(60 degrees) = 1/2. Therefore, cos^(-1)(1/2) = 60 degrees (or Ο€/3 radians).
  • Step 3: Now we need to find cot(60 degrees). Cotangent is the reciprocal of tangent.
  • Step 4: First, find tan(60 degrees). We know that tan(60 degrees) = √3.
  • Step 5: Now, calculate cot(60 degrees). Since cot(ΞΈ) = 1/tan(ΞΈ), we have cot(60 degrees) = 1/(√3).
  • Step 6: Simplify cot(60 degrees). The value of cot(60 degrees) is √3.
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