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What is the value of sec(θ) if cos(θ) = 3/5?

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Question: What is the value of sec(θ) if cos(θ) = 3/5?

Options:

  1. 5/3
  2. 3/5
  3. 4/5
  4. 1/3

Correct Answer: 5/3

Solution: 

sec(θ) = 1/cos(θ) = 1/(3/5) = 5/3.

What is the value of sec(θ) if cos(θ) = 3/5?

Practice Questions

Q1
What is the value of sec(θ) if cos(θ) = 3/5?
  1. 5/3
  2. 3/5
  3. 4/5
  4. 1/3

Questions & Step-by-Step Solutions

What is the value of sec(θ) if cos(θ) = 3/5?
Correct Answer: 5/3
  • 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/(3/5).
  • Step 4: To divide by a fraction, multiply by its reciprocal: sec(θ) = 1 * (5/3).
  • Step 5: Simplify the expression: sec(θ) = 5/3.
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