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What is the value of sec(θ) if cos(θ) = 1/3?

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Question: What is the value of sec(θ) if cos(θ) = 1/3?

Options:

  1. 3
  2. 1/3
  3. √3
  4. 1

Correct Answer: 3

Solution: 

sec(θ) = 1/cos(θ) = 1/(1/3) = 3.

What is the value of sec(θ) if cos(θ) = 1/3?

Practice Questions

Q1
What is the value of sec(θ) if cos(θ) = 1/3?
  1. 3
  2. 1/3
  3. √3
  4. 1

Questions & Step-by-Step Solutions

What is the value of sec(θ) if cos(θ) = 1/3?
  • Step 1: Understand that sec(θ) is the reciprocal of cos(θ).
  • Step 2: Write the formula for sec(θ): sec(θ) = 1/cos(θ).
  • Step 3: Substitute the given value of cos(θ) into the formula: sec(θ) = 1/(1/3).
  • Step 4: Simplify the expression: 1/(1/3) means you multiply 1 by the reciprocal of 1/3, which is 3.
  • Step 5: Therefore, sec(θ) = 3.
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