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What is the value of cos(2x) if sin x = 1/2?

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Question: What is the value of cos(2x) if sin x = 1/2?

Options:

  1. 1/2
  2. 0
  3. 1
  4. √3/2

Correct Answer: 1/2

Solution: 

Using the double angle formula cos(2x) = 1 - 2sin^2 x. Since sin x = 1/2, we have cos(2x) = 1 - 2*(1/2)^2 = 1 - 2*(1/4) = 1 - 1/2 = 1/2.

What is the value of cos(2x) if sin x = 1/2?

Practice Questions

Q1
What is the value of cos(2x) if sin x = 1/2?
  1. 1/2
  2. 0
  3. 1
  4. √3/2

Questions & Step-by-Step Solutions

What is the value of cos(2x) if sin x = 1/2?
  • Step 1: Identify the given value. We know that sin x = 1/2.
  • Step 2: Recall the double angle formula for cosine: cos(2x) = 1 - 2sin^2 x.
  • Step 3: Substitute the value of sin x into the formula. Since sin x = 1/2, we calculate sin^2 x: (1/2)^2 = 1/4.
  • Step 4: Now substitute sin^2 x back into the formula: cos(2x) = 1 - 2*(1/4).
  • Step 5: Calculate 2*(1/4) which equals 1/2.
  • Step 6: Now substitute this value back into the equation: cos(2x) = 1 - 1/2.
  • Step 7: Finally, calculate 1 - 1/2 to get cos(2x) = 1/2.
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