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Product-to-Sum and Sum-to-Product Formulas

Product-to-Sum and Sum-to-Product Formulas

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Product-to-Sum and Sum-to-Product Formulas

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  1. Product-to-Sum and Sum-to-Product Formulas

  2. Product-to-Sum Formulas • Changing an equation from a multiplication problem to an addition problem

  3. Expressing Products as Sums • Express each of the following products as a sum containing only sines or cosines. • (a) sin (6q) sin (4q) • (b) cos (3q) cos (q)

  4. Expressing Products as Sums • (c) sin (3q) cos (5q)

  5. Sum-to-Product Formulas • Changing equations from an addition problem to a multiplication problem

  6. Expressing Sums as a Product • Express each sum or difference as a product of sines and/or cosines. • (a) sin (5q) – sin (3q) • (b) sin (4q) + sin (2q)

  7. Expressing Sums as Products • (c) cos q – cos (3q) • (d) cos (5q) + cos (3q)

  8. Establishing Identities • Establish the identity

  9. Establishing Identities • Establish the identity

  10. Product-to-Sum and Sum-to-Product • On-line Tutorial • On-line Video