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   Introduction Introduction
   What's the essence? Essence
   Memorizing Memorizing

  Basic Formulas
  Sum and Difference Formulas
  Double & Triple Angle Formulas
  Half Angle Formulas
  Product to Sum Formulas
  Sum to Product Formulas
  All Formulas

   Understanding Understanding
   Summarizing Summarizing
   Examples Examples
   Exercises Exercises
   Final thoughts Final thoughts

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Product-to-Sum Formulas:

3_401.gif (8950 bytes)

Notice--the sine product and the cosine product have the same cosine expression with one negative and one positive. The cosine product becomes cosine sum, and sine product becomes cosine difference. Note the order of the subtractions: the cosine of the difference of the angles minus the cosine of the sum of the angles. Mixed sine and cosine product gives an all sine answer. The mixed product becomes a sine sum. Be aware of the order of al_m_bet.gif (1099 bytes) in the term 3_402.gif (1459 bytes), alpha.gif (882 bytes) is the angle of the sine function and beta.gif (942 bytes) is the angle of the cosine function in the mixed product.

Also, we need to memorize that when products go to sums, the angles alpha.gif (882 bytes) and beta.gif (942 bytes) become al_p_bet.gif (1116 bytes) and al_m_bet.gif (1099 bytes). Don't forget the coefficient 1_o_2.gif (960 bytes)'s in each formula.


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Copyright 1998 LWR, ThinkQuest team 17119. All rights reserved.