Trigonometry Formulas
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Questions and Answers

What is the formula for sin(2θ) in terms of θ?

  • 2sin(θ)cos(θ) (correct)
  • sin(θ)cos(θ)
  • sin(θ) - cos(θ)
  • sin²(θ) + cos²(θ)

    • What is the formula for cos(2θ) in terms of θ?

  • 2cos²(θ) - sin²(θ)
  • cos²(θ) - sin²(θ) (correct)
  • cos²(θ) + sin²(θ)
  • sin²(θ) - cos²(θ)

    • What is the formula for tan(θ/2) in terms of θ?

  • (1 - cos(θ)) / sin(θ) (correct)
  • sin(θ) / (1 - cos(θ))
  • ±√((1 + cos(θ))/(1 - cos(θ)))
  • ±√((1 - cos(θ))/(1 + cos(θ)))

    • What is the formula for sin(θ/2) in terms of θ?

    <p>±√((1 - cos(θ))/2)</p> Signup and view all the answers

    What is the formula for cos(θ/2) in terms of θ?

    <p>±√((1 + cos(θ))/2)</p> Signup and view all the answers

    Study Notes

    Trigonometric Identities

    Double Angle Formulas

    • Sine Double Angle Formula:
      • sin(2θ) = 2sin(θ)cos(θ)
    • Cosine Double Angle Formulas:
      • cos(2θ) = cos²(θ) - sin²(θ) = 1 - 2sin²(θ) = 2cos²(θ) - 1
    • Tangent Double Angle Formula:
      • tan(2θ) = 2tan(θ) / (1 - tan²(θ))

    Half Angle Formulas

    • Sine Half Angle Formula:
      • sin(θ/2) = ±√((1 - cos(θ))/2)
    • Cosine Half Angle Formula:
      • cos(θ/2) = ±√((1 + cos(θ))/2)
    • Tangent Half Angle Formula:
      • tan(θ/2) = ±√((1 - cos(θ))/(1 + cos(θ)))
      • tan(θ/2) = sin(θ) / (1 + cos(θ))
      • tan(θ/2) = (1 - cos(θ)) / sin(θ)

    Trigonometric Identities

    Double Angle Formulas

    • Double angle formulas are used to find the sine, cosine, and tangent of twice an angle.
    • Sine Double Angle Formula: sin(2θ) = 2sin(θ)cos(θ)
    • Cosine Double Angle Formulas: cos(2θ) has three forms:
      • cos²(θ) - sin²(θ)
      • 1 - 2sin²(θ)
      • 2cos²(θ) - 1
    • Tangent Double Angle Formula: tan(2θ) = 2tan(θ) / (1 - tan²(θ))

    Half Angle Formulas

    • Half angle formulas are used to find the sine, cosine, and tangent of half an angle.
    • Sine Half Angle Formula: sin(θ/2) = ±√((1 - cos(θ))/2)
    • Cosine Half Angle Formula: cos(θ/2) = ±√((1 + cos(θ))/2)
    • Tangent Half Angle Formula: tan(θ/2) has three forms:
      • ±√((1 - cos(θ))/(1 + cos(θ)))
      • sin(θ) / (1 + cos(θ))
      • (1 - cos(θ)) / sin(θ)

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    Test your knowledge of trigonometric identities, including double angle formulas and half angle formulas for sine, cosine, and tangent.

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