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Double Angle Identities quiz

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  • What is the double angle identity for sine?
    The double angle identity for sine is sin(2θ) = 2 sin(θ) cos(θ).
  • What is the double angle identity for cosine?
    The double angle identity for cosine is cos(2θ) = cos²(θ) - sin²(θ).
  • What is the double angle identity for tangent?
    The double angle identity for tangent is tan(2θ) = 2 tan(θ) / (1 - tan²(θ)).
  • How are double angle identities derived?
    They are derived from the sum formulas by using the same angle for both terms.
  • How can cos²(π/12) - sin²(π/12) be simplified using a double angle identity?
    It can be rewritten as cos(2 × π/12) = cos(π/6).
  • What is the value of cos(π/6)?
    The value of cos(π/6) is √3/2.
  • How can sin(15°) cos(15°) be rewritten using a double angle identity?
    It can be rewritten as sin(30°)/2 using the sine double angle identity.
  • What should you look for when deciding to use a double angle identity?
    Look for expressions that match or contain parts of the double angle identities.
  • What is an alternate form of the cosine double angle identity using only cosine?
    cos(2θ) = 2 cos²(θ) - 1.
  • What is an alternate form of the cosine double angle identity using only sine?
    cos(2θ) = 1 - 2 sin²(θ).
  • If you see an argument of 2θ in a trig expression, what identity should you consider using?
    You should consider using the double angle identities.
  • How can you express sin(θ) cos(θ) in terms of sin(2θ)?
    sin(θ) cos(θ) = sin(2θ)/2.
  • Why are double angle identities useful in trigonometry?
    They help simplify trig expressions and make it easier to solve problems.
  • What is the process for simplifying an expression like sin(15°) cos(15°) using identities?
    Recognize it as part of the sine double angle identity and rewrite it as sin(30°)/2.
  • What is the general strategy for simplifying trig expressions with identities?
    Scan for patterns that match known identities and rewrite the expression using those identities.