Gr12 Mathematics: Ch 4.2 Double Angle Identities

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Questions and Answers

What is the double angle formula for sine?

  • sin(2α) = 2 sinα cosα (correct)
  • sin(2α) = cos²α - sin²α
  • sin(2α) = sinα + cosα
  • sin(2α) = sin²α - cos²α

What is thealternate form of the cosine double angle formula derived from the Pythagorean identity?

  • cos(2α) = 1 + 2 sin²α
  • cos(2α) = 2 cos²α + 1
  • cos(2α) = cos²α + sin²α
  • cos(2α) = 1 - 2 sin²α (correct)

Which of the following is NOT a cosine double angle formula?

  • cos(2α) = sin²α - cos²α (correct)
  • cos(2α) = 1 - 2 sin²α
  • cos(2α) = cos²α - sin²α
  • cos(2α) = 2 cos²α - 1

What is the starting point for deriving the double angle formulas?

<p>Sum formulas for sine and cosine (D)</p> Signup and view all the answers

What is the result of letting α = β in the sum formula for sine?

<p>sin(2α) = 2 sinα cosα (A)</p> Signup and view all the answers

What is the double angle formula for cosine in terms of sine?

<p>cos(2α) = 1 - 2 sin²α (D)</p> Signup and view all the answers

How many valid forms of the cosine double angle formula are there?

<p>3 (A)</p> Signup and view all the answers

What is the purpose of the Pythagorean identity in deriving the double angle formulas?

<p>To derive alternate forms of the cosine double angle formula (D)</p> Signup and view all the answers

What is the common factor in the double angle formulas for sine and cosine?

<p>2 (B)</p> Signup and view all the answers

What is the purpose of using the Pythagorean identity in deriving the double angle formulas?

<p>To provide an alternative form for the cosine double angle formula (B)</p> Signup and view all the answers

Which of the following is a consequence of the double angle formulas?

<p>sin(2α) = 0 when α = 0 (A)</p> Signup and view all the answers

What is the relationship between the sum formulas for sine and cosine and the double angle formulas?

<p>The sum formulas are used to derive the double angle formulas (B)</p> Signup and view all the answers

What is the advantage of having multiple forms of the cosine double angle formula?

<p>It provides more flexibility in solving problems (D)</p> Signup and view all the answers

Which of the following is NOT a direct consequence of the double angle formulas?

<p>sin(2α) = 2 when α = π/2 (D)</p> Signup and view all the answers

What is the main difference between the double angle formulas for sine and cosine?

<p>The sine double angle formula involves the product of sine and cosine (B)</p> Signup and view all the answers

Which of the following is a common application of the double angle formulas?

<p>Simplifying trigonometric expressions (B)</p> Signup and view all the answers

What is the key insight in deriving the double angle formula for sine?

<p>Using the sum formula for sine with α = β (C)</p> Signup and view all the answers

What is the key property of the double angle formulas that allows them to be used in various trigonometric identities?

<p>They can be expressed in terms of sine and cosine (D)</p> Signup and view all the answers

What is the reason for having multiple forms of the cosine double angle formula?

<p>To provide flexibility in using the formula in different situations (D)</p> Signup and view all the answers

What is the relationship between the sum formulas for sine and cosine and the double angle formulas?

<p>The sum formulas are used to derive the double angle formulas (B)</p> Signup and view all the answers

What is the consequence of the double angle formulas in terms of simplifying trigonometric expressions?

<p>They can be used to simplify trigonometric expressions involving double angles (D)</p> Signup and view all the answers

What is the benefit of using the Pythagorean identity in deriving the double angle formulas?

<p>It allows us to express the formulas in terms of sine and cosine (C)</p> Signup and view all the answers

How do the double angle formulas for sine and cosine differ?

<p>The sine formula involves a product, while the cosine formula involves a sum (A)</p> Signup and view all the answers

What is the main application of the double angle formulas?

<p>Simplifying trigonometric expressions involving double angles (B)</p> Signup and view all the answers

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