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Exploring Product and Sum Identities in Trigonometry: Forms and Applications

Dive into the fascinating world of trigonometric identities with a focus on product and sum identities. Learn how these identities can be expressed in two forms by adding or subtracting either the sum or the difference identities. This lesson includes practical examples that demonstrate how to convert products to sums and vice versa. Additionally, important properties of sine and cosine regarding their oddness and evenness are highlighted. Engage in partner activities and homework exercises to solidify your understanding of these key concepts.

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Exploring Product and Sum Identities in Trigonometry: Forms and Applications

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Presentation Transcript

  1. 6.4 Product / Sum Identities

  2. Product / Sum Identities have 2 forms! - They can be derived by adding or subtracting the sum or difference identities. Product / Sum Identities

  3. Alternate Form

  4. Ex 1) Express the product as a sum or difference.

  5. Ex 2) Express the sum as a product. what happened to the (–) ? cos is even cos (–x) = cos (x) and just in case … sin is odd sin (–x) = – sin (x)

  6. Try with a partner!! Ex 3) Prove:

  7. Homework • HW Hints & Even Answers: • 21 & 22: eqtn you need is in paragraph above question – read!! • 22: 15.9° • 26 & 27: (proof  - start on RHS & use identities from section 6-1) • 38: • 40: • 44 & 45: (proof  - start on LHS and use fact that you can divide both sides of identity by 2) #603 Pg 309 #1–17 odd, 21–23, 25–27, 38, 40, 44, 45 use the alternate form of product/sum identities

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