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

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

Options:

  1. 1/2
  2. 0
  3. -1/2
  4. 1

Correct Answer: -1/2

Solution: 

Using the double angle formula cos(2θ) = 1 - 2sin^2 θ. Here, sin θ = 1/2, so cos(2θ) = 1 - 2(1/2)^2 = 1 - 2(1/4) = 1 - 1/2 = 1/2.

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

Practice Questions

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

Questions & Step-by-Step Solutions

What is the value of cos(2θ) if sin θ = 1/2?
  • Step 1: Identify the value of sin θ. We know that sin θ = 1/2.
  • Step 2: Use the double angle formula for cosine: cos(2θ) = 1 - 2sin^2 θ.
  • Step 3: Substitute the value of sin θ into the formula: cos(2θ) = 1 - 2(1/2)^2.
  • Step 4: Calculate (1/2)^2, which is 1/4.
  • Step 5: Substitute this value back into the equation: cos(2θ) = 1 - 2(1/4).
  • Step 6: Multiply 2 by 1/4 to get 1/2: cos(2θ) = 1 - 1/2.
  • Step 7: Finally, subtract 1/2 from 1 to find cos(2θ): cos(2θ) = 1/2.
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