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   Final thoughts

4. Understanding the formulas--Page 2

We know the Double-Angle formula of cosine:

4_201.gif (3690 bytes)

which show us the relationship between angles theta.gif (908 bytes) and 2theta.gif (991 bytes). These three presentations are not different essentially. Using the formula sin_cos1.gif (1861 bytes), we can get one form from other two forms. Now from the idea of transforming the three differences, we understand how to use these three formulas. If we want to transform 2theta.gif (991 bytes) to theta.gif (908 bytes) and cosine to sine, we use the second form. If we want to change 2theta.gif (991 bytes) to theta.gif (908 bytes) and keep the function cosine, we use the third form, if we want to change 2theta.gif (991 bytes) to theta.gif (908 bytes) and cosine to cosine and sine we use the first form.

The Sum to Product formulas are as following:

4_202.gif (10023 bytes)

In section 3, we told you how to memorize these four formulas. Of course, the first role of these formulas is changing sum to product from the left to the right. Now we need to know what kinds of functions can transform to the others, and as well as the angles. From the formulas we see, sine plus or minus sine changes to sine times cosine; cosine plus cosine to cosine times cosine; cosine minus cosine to sine times sine; and alpha.gif (882 bytes), beta.gif (942 bytes)to a_p_b_2.gif (1184 bytes) and a_m_b_2.gif (1151 bytes).

We can not explain every formula for you. We believe that you can analyze every formula like we did. After you read our eliciting explanation above, please complete the analysis of all formulas, which is important for you to solve problems.


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