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[Index]

Introduction
Essence
Memorizing
How to memorize
Basic Formulas
Sum and Difference Formulas
Double & Triple Angle Formulas
Half Angle Formulas
Product to Sum Formulas
Sum to Product Formulas
All Formulas
Understanding
Page 1
Page 2
Page 3
Page 4
Page 5
Summarizing
Page 1
Page 2
Examples
Examples
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
Example 7
Example 8
General ideas
Exercises
Final thoughts
     
remember


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Sum-to-Product Formulas:

3_501.gif (9941 bytes)

Notice--cosine sums have all cosine product or all sine product answers and sine sums have the mixed products of sine and cosine. When sums go to products the angles alpha.gif (882 bytes) and beta.gif (942 bytes) become a_p_b_2.gif (1184 bytes) and a_m_b_2.gif (1151 bytes). Note the distribution of angles and functions, and what formula has coefficient -2.

3_502.gif (5422 bytes)

In formulas 1 and 2, be aware the order of functions in the products: cosine is behind sine. And the order of angles, sine plus sine gives the first factor 3_503.gif (1358 bytes) and the second is 3_504.gif (1303 bytes). sine minus sine makes the first factor 3_505.gif (1338 bytes) and the second 3_506.gif (1357 bytes).

3_507.gif (5645 bytes)

In formulas 3 and 4, the sum of cosines of alpha.gif (882 bytes) and beta.gif (942 bytes) become the product of cosines of a_p_b_2.gif (1184 bytes) and a_m_b_2.gif (1151 bytes). The differences of cosines of alpha.gif (882 bytes) and beta.gif (942 bytes) become the product of sines of a_p_b_2.gif (1184 bytes) and a_m_b_2.gif (1151 bytes). Note al_m_bet.gif (1099 bytes) in 3_505.gif (1338 bytes) and 3_508.gif (1493 bytes) have the same order, and the coefficient is negative 2, which is different from other three formulas.

We hope you can memorize all these formulas effectively, because they are really important. After you think you know all of them then go to Understanding the Formulas section to learn more about them. Or if you need more information about the basic trigonometric formulas, then come here for more information. Good luck.


     
  

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