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

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

Options:

  1. 1/√2
  2. 1
  3. √2/2
  4. √2

Correct Answer: 1

Solution: 

Using the double angle formula, sin(2θ) = 2sin(θ)cos(θ) = 2(1/√2)(1/√2) = 1.

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

Practice Questions

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

Questions & Step-by-Step Solutions

What is the value of sin(2θ) if sin(θ) = 1/√2?
Correct Answer: 1
  • Step 1: Identify the given value. We have sin(θ) = 1/√2.
  • Step 2: Recall the double angle formula for sine: sin(2θ) = 2sin(θ)cos(θ).
  • Step 3: We already know sin(θ) = 1/√2. Now we need to find cos(θ).
  • Step 4: Use the Pythagorean identity: sin²(θ) + cos²(θ) = 1.
  • Step 5: Substitute sin(θ) into the identity: (1/√2)² + cos²(θ) = 1.
  • Step 6: Calculate (1/√2)², which is 1/2. So, 1/2 + cos²(θ) = 1.
  • Step 7: Solve for cos²(θ): cos²(θ) = 1 - 1/2 = 1/2.
  • Step 8: Take the square root to find cos(θ): cos(θ) = 1/√2 (we take the positive root).
  • Step 9: Now substitute sin(θ) and cos(θ) back into the double angle formula: sin(2θ) = 2(1/√2)(1/√2).
  • Step 10: Calculate the product: 2(1/√2)(1/√2) = 2 * (1/2) = 1.
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