[Index]
- Introduction
- Essence
- Memorizing
- Understanding
- Summarizing
- Examples
- Exercises
- Final thoughts
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4. Understanding the formulas--Page 2
We know the Double-Angle formula of cosine:
which show us
the relationship between angles 
and 
. These three presentations are not different
essentially. Using the formula 
, 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 to and cosine to sine,
we use the second form. If we want to change to and keep the
function cosine, we use the third
form, if we want to change to and cosine to
cosine and sine we use the first form.
The Sum to Product formulas are as following:
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 
, 
to 
and 
.
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.
