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What is the value of sin(2θ) in terms of sin(θ) and cos(θ)?

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Question: What is the value of sin(2θ) in terms of sin(θ) and cos(θ)?

Options:

  1. 2sin(θ)cos(θ)
  2. sin^2(θ) + cos^2(θ)
  3. sin(θ) + cos(θ)
  4. sin(θ)cos(θ)

Correct Answer: 2sin(θ)cos(θ)

Solution: 

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

What is the value of sin(2θ) in terms of sin(θ) and cos(θ)?

Practice Questions

Q1
What is the value of sin(2θ) in terms of sin(θ) and cos(θ)?
  1. 2sin(θ)cos(θ)
  2. sin^2(θ) + cos^2(θ)
  3. sin(θ) + cos(θ)
  4. sin(θ)cos(θ)

Questions & Step-by-Step Solutions

What is the value of sin(2θ) in terms of sin(θ) and cos(θ)?
  • Step 1: Understand that sin(2θ) means the sine of double the angle θ.
  • Step 2: Recall the double angle formula for sine, which states that sin(2θ) can be expressed in terms of sin(θ) and cos(θ).
  • Step 3: The double angle formula is sin(2θ) = 2 * sin(θ) * cos(θ).
  • Step 4: Therefore, you can write sin(2θ) as 2sin(θ)cos(θ).
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